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0001 @article{Doplicher:1965,
0002         abstract = {It is shown that a translationally invariant algebra A of local obser- vables (see [1]) admits a representation in a Hubert space having a vacuum state. Furthermore an algebraic criterion is given which is necessary and sufficient for the existence of at least one representation of A in which the usual spectral condition for the energy-momentum operators holds.},
0003         author = {S. Doplicher},
0004         journal = {Commun. Math. Phys.},
0005         pages = {1--5},
0006         slaccitation = {\%\%CITATION = CMPHA,16,138\\;\%\%},
0007         title = {{An algebraic spectrum condition}},
0008         url = {http://projecteuclid.org/euclid.cmp/1103757611},
0009         volume = {1},
0010         year = {1965}
0011 }
0012 
0013 @article{Borchers:1969,
0014         abstract = {Let A be a C*-algebra and G be a locally compact group acting as strongly continuous automorphisms on si. Let π be a representation of s/ then we say π is a co- variant representation if there exists a strongly continuous unitary representation of the group acting on H\_π which implements the automorphisms. We give necessary and sufficient conditions on a representation π of si such that a) π is subrepresentation of a covariant representation and b) π is subrepresentation of a covariant representation quasi-equivalent to π.},
0015         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
0016         journal = {Commun. Math. Phys.},
0017         localfile = {1969 - Borchers - On the Implementability of Automorphism Groups.pdf},
0018         pages = {305--314},
0019         slaccitation = {\%\%CITATION = CMPHA,14,305\\;\%\%},
0020         title = {{On the implementability of automorphism groups}},
0021         url = {http://projecteuclid.org/euclid.cmp/1103841819},
0022         volume = {14},
0023         year = {1969}
0024 }
0025 
0026 @article{EpsteinGlaserMartin:1969,
0027         abstract = {It is shown that, in theories of exactly localized observables, of the type proposed by Araki and Haag , the reaction amplitude for two particles giving two particles is polynomially bounded in s for fixed momentum transfer t < 0. The proof does not need observables localized in space-time regions of arbitrarily small volume, but uses relativistic invariance in an essential way. I t is given for the case of spinless neutral particles, but is easily extendable to all cases of charge and spin. The proof can also be generalized to the case of particles described by regularized products [...] of Wightman or Jaffe fields.},
0028         author = {H. Epstein and V. Glaser and A. Martin},
0029         journal = {Commun. Math. Phys.},
0030         localfile = {1969 - Epstein, Glaser, Martin - Polynomial behaviour of scattering amplitudes at fixed momentum transfer in theories with local observables.pdf},
0031         pages = {257--316},
0032         slaccitation = {\%\%CITATION = CMPHA,13,257\\;\%\%},
0033         title = {{Polynomial behaviour of scattering amplitudes at fixed momentum transfer in theories with local observables}},
0034         url = {http://projecteuclid.org/euclid.cmp/1103841627},
0035         volume = {13},
0036         year = {1969}
0037 }
0038 
0039 @article{GlimmJaffe:1971-1,
0040         abstract = {We prove that the P(φ)\_2 quantum field theory satisfies the spectral condition. The space time translation a = (x, t) is implemented by the unitary group U(a) = exp(ίtH ----------------------------------------------------------------------------- ixP), and the joint spectrum of the energy operator H and the momentum operator P is contained in the forward cone. We also obtain bounds on certain vacuum expectation values of products of field operators. Our proofs involve an analysis of the limit V->-oo for approximate theories in a periodic box of volume V. Assuming the existence of a uniform mass gap, we are able to establish all the Wightman axioms with the exception of the Lorentz invariance of the vacuum.},
0041         author = {J. Glimm and A. Jaffe},
0042         journal = {Commun. Math. Phys.},
0043         localfile = {1971 - Glimm, Jaffe - The energy momentum spectrum and vacuum expectation values in quantum field theory II.pdf},
0044         pages = {1--22},
0045         slaccitation = {\%\%CITATION = CMPHA,22,1\\;\%\%},
0046         title = {{The energy momentum spectrum and vacuum expectation values in quantum field theory, ii}},
0047         url = {http://projecteuclid.org/euclid.cmp/1103857409},
0048         volume = {22},
0049         year = {1971}
0050 }
0051 
0052 @article{BorchersHegerfeldt:1972,
0053         abstract = {Let T be a one-to-one mapping of n-dimensional space-time M onto itself. If T maps light cones onto light cones and dim M >= 3, it is shown that T is, up to a scale factor, an inhomogeneous Lorentz transformation. Thus constancy of light velocity alone implies the Lorentz group (up to dilatations). The same holds if T and T'1 preserve (x ----------------------------------------------------------------------------- y)^2 > 0. This generalizes Zeeman's Theorem. It is then shown that if T maps lightlike lines onto (arbitrary) straight lines and if dimM >= 3, then T is linear. The last result can be applied to transformations connecting different reference frames in a relativistic or non-relativistic theory.},
0054         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and G. C. Hegerfeldt},
0055         journal = {Commun. Math. Phys.},
0056         localfile = {1972 - Borchers, Hegerfeldt - The Structure of Space-Time Transformations.pdf},
0057         pages = {259--266},
0058         slaccitation = {\%\%CITATION = CMPHA,28,259\\;\%\%},
0059         title = {{The structure of space-time transformations}},
0060         url = {http://projecteuclid.org/euclid.cmp/1103858408},
0061         volume = {28},
0062         year = {1972}
0063 }
0064 
0065 @article{Woronowicz:1972,
0066         author = {S. L. Woronowicz},
0067         journal = {Commun. Math. Phys.},
0068         localfile = {1972 - Woronowicz - On the Purification of Factor States.pdf},
0069         pages = {221--235},
0070         slaccitation = {\%\%CITATION = CMPHA,28,221\\;\%\%},
0071         title = {{On the purification of factor states}},
0072         volume = {28},
0073         year = {1972}
0074 }
0075 
0076 @article{Buchholz:1975-1,
0077         author = {D. Buchholz},
0078         journal = {Commun. Math. Phys.},
0079         localfile = {1974 - Buchholz - Collision theory for massless Fermions.pdf},
0080         pages = {269},
0081         slaccitation = {\%\%CITATION = CMPHA,42,269\\;\%\%},
0082         title = {{Collision Theory for Massless Fermions}},
0083         volume = {42},
0084         year = {1975}
0085 }
0086 
0087 @article{Buchholz:1974-1,
0088         author = {D. Buchholz},
0089         journal = {Commun. Math. Phys.},
0090         localfile = {1974 - Buchholz - Haag-Ruelle approximation of collision states.pdf},
0091         pages = {243--253},
0092         slaccitation = {\%\%CITATION = CMPHA,36,243\\;\%\%},
0093         title = {{Haag-ruelle approximation of collision states}},
0094         volume = {36},
0095         year = {1974}
0096 }
0097 
0098 @article{Buchholz:1974-2,
0099         author = {D. Buchholz},
0100         journal = {Commun. Math. Phys.},
0101         localfile = {1974 - Buchholz - Product states for local algebras.pdf},
0102         pages = {287--304},
0103         slaccitation = {\%\%CITATION = CMPHA,36,287\\;\%\%},
0104         title = {{Product States for Local Algebras}},
0105         volume = {36},
0106         year = {1974}
0107 }
0108 
0109 @article{FannesVerbeure:1974,
0110         author = {M. Fannes and A. Verbeure},
0111         journal = {Commun. Math. Phys.},
0112         localfile = {1974 - Fannes, Verbeure - On the time evolution automorphisms of the CCR-algebra for quantum mechanics.pdf},
0113         pages = {257--264},
0114         slaccitation = {\%\%CITATION = CMPHA,35,257\\;\%\%},
0115         title = {{On the time evolution automorphisms of the ccr-algebra for quantum mechanics}},
0116         volume = {35},
0117         year = {1974}
0118 }
0119 
0120 @article{BorchersSen:1975,
0121         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and R. N. Sen},
0122         journal = {Commun. Math. Phys.},
0123         localfile = {1975 - Borchers, Sen - Relativity groups in the presence of matter.pdf},
0124         pages = {101},
0125         slaccitation = {\%\%CITATION = CMPHA,42,101\\;\%\%},
0126         title = {{Relativity Groups in the Presence of Matter}},
0127         volume = {42},
0128         year = {1975}
0129 }
0130 
0131 @article{BorchersYngvason:1975,
0132         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and J. Yngvason},
0133         journal = {Commun. Math. Phys.},
0134         localfile = {1975 - Borchers, Yngvason - Integral representations for Schwinger functionals and the moment problem over nuclear spaces.pdf},
0135         pages = {255},
0136         slaccitation = {\%\%CITATION = CMPHA,43,255\\;\%\%},
0137         title = {{Integral Representations for Schwinger Functionals and the Moment Problem over Nuclear Spaces}},
0138         volume = {43},
0139         year = {1975}
0140 }
0141 
0142 @article{BorchersYngvason:1975-1,
0143         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and J. Yngvason},
0144         journal = {Commun. Math. Phys.},
0145         localfile = {1975 - Borchers, Yngvason - On the algebra of field operators. The weak commutant and integral decompositions of states.pdf},
0146         pages = {231},
0147         slaccitation = {\%\%CITATION = CMPHA,42,231\\;\%\%},
0148         title = {{On the Algebra of Field Operators: The Weak Commutant and Integral Decompositions of States}},
0149         volume = {42},
0150         year = {1975}
0151 }
0152 
0153 @article{Driessler:1975,
0154         author = {W. Driessler},
0155         journal = {Commun. Math. Phys.},
0156         localfile = {1975 - Driessler - Comments on lightlike translations and applications in relativistic quantum field theory.pdf},
0157         pages = {133--141},
0158         slaccitation = {\%\%CITATION = CMPHA,44,133\\;\%\%},
0159         title = {{Comments on Lightlike Translations and Applications in Relativistic Quantum Field Theory}},
0160         volume = {44},
0161         year = {1975}
0162 }
0163 
0164 @article{BorchersYngvason:1976,
0165         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and J. Yngvason},
0166         journal = {Commun. Math. Phys.},
0167         localfile = {1976 - Borchers, Yngvason - Necessary and sufficient conditions for integral representations of Wightman functionals at Schwinger points.pdf},
0168         pages = {197},
0169         slaccitation = {\%\%CITATION = CMPHA,47,197\\;\%\%},
0170         title = {{Necessary and Sufficient Conditions for Integral Representations of Wightman Functionals at Schwinger Points}},
0171         volume = {47},
0172         year = {1976}
0173 }
0174 
0175 @article{BuchholzRoberts:1976,
0176         author = {D. Buchholz and J. E. Roberts},
0177         journal = {Commun. Math. Phys.},
0178         localfile = {1976 - Buchholz, Roberts - Bounded perturbations of dynamics.pdf},
0179         pages = {161},
0180         slaccitation = {\%\%CITATION = CMPHA,49,161\\;\%\%},
0181         title = {{Bounded Perturbations of Dynamics}},
0182         volume = {49},
0183         year = {1976}
0184 }
0185 
0186 @article{Buchholz:1977,
0187         author = {D. Buchholz},
0188         journal = {Commun. Math. Phys.},
0189         localfile = {1977 - Buchholz - Collision theory for massless bosons.pdf},
0190         pages = {147},
0191         slaccitation = {\%\%CITATION = CMPHA,52,147\\;\%\%},
0192         title = {{Collision Theory for Massless Bosons}},
0193         volume = {52},
0194         year = {1977}
0195 }
0196 
0197 @article{BuchholzFredenhagen:1977,
0198         author = {D. Buchholz and K. Fredenhagen},
0199         journal = {Commun. Math. Phys.},
0200         localfile = {1977 - Buchholz, Fredenhagen - A note on the inverse scattering problem in quantum field theory.pdf},
0201         pages = {91},
0202         slaccitation = {\%\%CITATION = CMPHA,56,91\\;\%\%},
0203         title = {{A Note on the Inverse Scattering Problem in Quantum Field Theory}},
0204         volume = {56},
0205         year = {1977}
0206 }
0207 
0208 @article{Iagolnitzer:1978,
0209         author = {D. Iagolnitzer},
0210         journal = {Phys. Rev.},
0211         localfile = {1978 - Iagolnitzer - Factorization of the multiparticle S-matrix in two-dimensional space-time models.pdf},
0212         pages = {1275},
0213         slaccitation = {\%\%CITATION = PHRVA,D18,1275\\;\%\%},
0214         title = {{Factorization of the Multiparticle S-Matrix in two-dimensional Space-Time Models}},
0215         volume = {D18},
0216         year = {1978}
0217 }
0218 
0219 @article{PuszWoronowicz:1978,
0220         author = {W. Pusz and S. L. Woronowicz},
0221         journal = {Commun. Math. Phys.},
0222         localfile = {1978 - Pusz, Woronowicz - Passive States and KMS States for General Quantum Systems.pdf},
0223         pages = {273--290},
0224         slaccitation = {\%\%CITATION = CMPHA,58,273\\;\%\%},
0225         title = {{Passive States and KMS States for General Quantum Systems}},
0226         volume = {58},
0227         year = {1978}
0228 }
0229 
0230 @article{ShankarWitten:1978,
0231         author = {R. Shankar and E. Witten},
0232         journal = {Phys. Rev.},
0233         localfile = {1978 - Shankar, Witten - S-matrix of the supersymmetric nonlinear sigma model.pdf},
0234         pages = {2134},
0235         slaccitation = {\%\%CITATION = PHRVA,D17,2134\\;\%\%},
0236         title = {{THE S MATRIX OF THE SUPERSYMMETRIC NONLINEAR sigma MODEL}},
0237         volume = {D17},
0238         year = {1978}
0239 }
0240 
0241 @article{Longo:1979,
0242         author = {R. Longo},
0243         journal = {Commun. Math. Phys.},
0244         localfile = {1979 - Longo - Notes on algebraic invariants for noncommutative dynamical systems.pdf},
0245         pages = {195--207},
0246         slaccitation = {\%\%CITATION = CMPHA,69,195\\;\%\%},
0247         title = {{Notes on algebraic invariants for noncommutative dynamical systems}},
0248         volume = {69},
0249         year = {1979}
0250 }
0251 
0252 @article{EpsteinGlaserIagolnitzer:1981,
0253         author = {H. Epstein and V. Glaser and D. Iagolnitzer},
0254         journal = {Commun. Math. Phys.},
0255         localfile = {1981 - Epstein, Glaser, Iagolnitzer - SOME ANALYTICITY PROPERTIES ARISING FROM ASYMPTOTIC COMPLETENESS IN QUANTUM FIELD THEORY.pdf},
0256         pages = {99},
0257         slaccitation = {\%\%CITATION = CMPHA,80,99\\;\%\%},
0258         title = {{SOME ANALYTICITY PROPERTIES ARISING FROM ASYMPTOTIC COMPLETENESS IN QUANTUM FIELD THEORY}},
0259         volume = {80},
0260         year = {1981}
0261 }
0262 
0263 @article{Emch:1981,
0264         author = {G. G. Emch},
0265         journal = {Int. J. Theor. Phys.},
0266         localfile = {1981 - Emch - Prequantization and KMS structures.pdf},
0267         pages = {891--904},
0268         slaccitation = {\%\%CITATION = IJTPB,20,891\\;\%\%},
0269         title = {{PREQUANTIZATION AND KMS STRUCTURES}},
0270         volume = {20},
0271         year = {1981}
0272 }
0273 
0274 @article{Buchholz:1982,
0275         author = {D. Buchholz},
0276         journal = {Commun. Math. Phys.},
0277         localfile = {1982 - Buchholz - THE PHYSICAL STATE SPACE OF QUANTUM ELECTRODYNAMICS.pdf},
0278         pages = {49},
0279         slaccitation = {\%\%CITATION = CMPHA,85,49\\;\%\%},
0280         title = {{THE PHYSICAL STATE SPACE OF QUANTUM ELECTRODYNAMICS}},
0281         volume = {85},
0282         year = {1982}
0283 }
0284 
0285 @article{HislopLongo:1982,
0286         author = {P. D. Hislop and R. Longo},
0287         journal = {Commun. Math. Phys.},
0288         localfile = {1982 - Hislop, Longo - Modular structure of the local algebras associated with the free massless scalar field theory.pdf},
0289         pages = {71},
0290         slaccitation = {\%\%CITATION = CMPHA,84,71\\;\%\%},
0291         title = {{Modular Structure of the Local Algebras Associated with the Free Massless Scalar Field Theory}},
0292         volume = {84},
0293         year = {1982}
0294 }
0295 
0296 @article{Steinmann:1982,
0297         author = {O. Steinmann},
0298         journal = {Commun. Math. Phys.},
0299         localfile = {1982 - Steinmann - A JOST-SCHROER THEOREM FOR STRING FIELDS.pdf},
0300         pages = {259},
0301         slaccitation = {\%\%CITATION = CMPHA,87,259\\;\%\%},
0302         title = {{A {J}OST-{S}CHROER THEOREM FOR STRING FIELDS}},
0303         volume = {87},
0304         year = {1982}
0305 }
0306 
0307 @article{DoplicherLongo:1983,
0308         author = {S. Doplicher and R. Longo},
0309         journal = {Commun. Math. Phys.},
0310         localfile = {1983 - Doplicher, Longo - LOCAL ASPECTS OF SUPERSELECTION RULES. II.pdf},
0311         pages = {399--409},
0312         slaccitation = {\%\%CITATION = CMPHA,88,399\\;\%\%},
0313         title = {{Local Aspects of Superselection Rules II}},
0314         volume = {88},
0315         year = {1983}
0316 }
0317 
0318 @article{Wichmann:1983,
0319         author = {E. H. Wichmann},
0320         journal = {J. Math. Phys.},
0321         localfile = {1983 - Wichmann - ON SYSTEMS OF LOCAL OPERATORS AND THE DUALITY CONDITION.pdf},
0322         pages = {1633--1644},
0323         slaccitation = {\%\%CITATION = JMAPA,24,1633\\;\%\%},
0324         title = {{ON SYSTEMS OF LOCAL OPERATORS AND THE DUALITY CONDITION}},
0325         volume = {24},
0326         year = {1983}
0327 }
0328 
0329 @article{BaumgrtelWollenberg:1984,
0330         author = {H. Baumg{\"{a}}rtel and M. Wollenberg},
0331         journal = {Commun. Math. Phys.},
0332         localfile = {1984 - Baumg\"{a}rtel, Wollenberg - A class of nontrivial weakly local massive Wightman fields with interpolating properties.pdf},
0333         pages = {331--352},
0334         slaccitation = {\%\%CITATION = CMPHA,94,331\\;\%\%},
0335         title = {{A CLASS OF NONTRIVIAL WEAKLY LOCAL MASSIVE {W}IGHTMAN FIELDS WITH INTERPOLATING PROPERTIES}},
0336         volume = {94},
0337         year = {1984}
0338 }
0339 
0340 @article{Borchers:1984,
0341         abstract = {Abstract. Let {A, Ud, α} be a C*-dynamical system, where Ud is the ^-dimen- sional vector group. Let V be a convex cone in Ud and V its dual cone. We will characterize those representations of A with the properties (i)αα, aeUd is weakly inner, (ii) the corresponding unitary representation U(a) is continuous, and (iii) the spectrum of U(a) is contained in V.},
0342         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
0343         journal = {Commun. Math. Phys.},
0344         localfile = {1984 - Borchers - Translation Group and Spectrum Condition.pdf},
0345         pages = {1--13},
0346         title = {{Translation group and Spectrum Condition}},
0347         volume = {96},
0348         year = {1984}
0349 }
0350 
0351 @article{BorchersBuchholz:1985,
0352         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and D. Buchholz},
0353         journal = {Commun. Math. Phys.},
0354         localfile = {1985 - Borchers, Buchholz - The Energy-Momentum Spectrum in Local Field Theories with Broken Lorentz-Symmetry.pdf},
0355         pages = {169},
0356         slaccitation = {\%\%CITATION = CMPHA,97,169\\;\%\%},
0357         title = {{THE ENERGY MOMENTUM SPECTRUM IN LOCAL FIELD THEORIES WITH BROKEN LORENTZ SYMMETRY}},
0358         volume = {97},
0359         year = {1985}
0360 }
0361 
0362 @article{BuchholzEpstein:1985,
0363         author = {D. Buchholz and H. Epstein},
0364         journal = {Fizika},
0365         localfile = {1985 - Buchholz, Epstein - Spin and Statistics of Quantum Topological Charges.pdf},
0366         pages = {329},
0367         slaccitation = {\%\%CITATION = FZKAA,17,329\\;\%\%},
0368         title = {{SPIN AND STATISTICS OF QUANTUM TOPOLOGICAL CHARGES}},
0369         volume = {17},
0370         year = {1985}
0371 }
0372 
0373 @article{BuchholzJunglas:1986,
0374         author = {D. Buchholz and P. Junglas},
0375         journal = {Lett. Math. Phys.},
0376         localfile = {1986 - Buchholz, Junglas - LOCAL PROPERTIES OF EQUILIBRIUM STATES AND THE PARTICLE SPECTRUM IN QUANTUM FIELD THEORY.pdf},
0377         pages = {51},
0378         slaccitation = {\%\%CITATION = LMPHD,11,51\\;\%\%},
0379         title = {{LOCAL PROPERTIES OF EQUILIBRIUM STATES AND THE PARTICLE SPECTRUM IN QUANTUM FIELD THEORY}},
0380         volume = {11},
0381         year = {1986}
0382 }
0383 
0384 @article{DriesslerSummersWichmann:1986,
0385         author = {W. Driessler and S. J. Summers and E. H. Wichmann},
0386         doi = {10.1007/BF01212341},
0387         journal = {Commun. Math. Phys.},
0388         localfile = {1986 - Driessler, Summers, Wichmann - On the connection between quantum fields and von Neumann algebras of local operators.pdf},
0389         pages = {49--84},
0390         slaccitation = {\%\%CITATION = CMPHA,105,49\\;\%\%},
0391         title = {{On the Connection between Quantum Fields and von Neumann Algebras of Local Operators}},
0392         volume = {105},
0393         year = {1986}
0394 }
0395 
0396 @article{PohlmeyerRehren:1986,
0397         author = {K. Pohlmeyer and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
0398         journal = {Commun. Math. Phys.},
0399         localfile = {1986 - Pohlmeyer, Rehren - ALGEBRAIC PROPERTIES OF THE INVARIANT CHARGES OF THE NAMBU- GOTO THEORY.pdf},
0400         pages = {593},
0401         slaccitation = {\%\%CITATION = CMPHA,105,593\\;\%\%},
0402         title = {{ALGEBRAIC PROPERTIES OF THE INVARIANT CHARGES OF THE NAMBU- GOTO THEORY}},
0403         volume = {105},
0404         year = {1986}
0405 }
0406 
0407 @article{BuchholzFredenhagenDAntoni:1987,
0408         author = {D. Buchholz and K. Fredenhagen and C. D'Antoni},
0409         journal = {Commun. Math. Phys.},
0410         localfile = {1987 - Buchholz, D'Antoni, Fredenhagen - The universal structure of local algebras.pdf},
0411         pages = {123},
0412         slaccitation = {\%\%CITATION = CMPHA,111,123\\;\%\%},
0413         title = {{The universal structure of local algebras}},
0414         volume = {111},
0415         year = {1987}
0416 }
0417 
0418 @article{BuchholzJacobi:1987,
0419         abstract = {It is shown that quantum field theories of free massless particles satisfy a recently proposed 'nuclearity condition' restricting the admissible number of local degrees of freedom of a theory. This result is based on an improved bound for the 'nuelearity index' of certain specific sets of vectors in Fock space.},
0420         author = {D. Buchholz and P. Jacobi},
0421         journal = {Lett. Math. Phys.},
0422         localfile = {1987 - Buchholz, Jacobi - On the Nuclearity Condition for Massless Fields.pdf},
0423         pages = {313},
0424         slaccitation = {\%\%CITATION = LMPHD,13,313\\;\%\%},
0425         title = {{On the Nuclearity Condition for Massless Fields}},
0426         volume = {13},
0427         year = {1987}
0428 }
0429 
0430 @article{PohlmeyerRehren:1988-1,
0431         author = {K. Pohlmeyer and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
0432         journal = {Commun. Math. Phys.},
0433         localfile = {1988 - Pohlmeyer, Rehren - THE ALGEBRA FORMED BY THE INVARIANT CHARGES OF THE NAMBU- GOTO THEORY: IDENTIFICATION OF A MAXIMAL ABELIAN SUBALGEBRA.pdf},
0434         pages = {55},
0435         slaccitation = {\%\%CITATION = CMPHA,114,55\\;\%\%},
0436         title = {{THE ALGEBRA FORMED BY THE INVARIANT CHARGES OF THE NAMBU- GOTO THEORY: IDENTIFICATION OF A MAXIMAL ABELIAN SUBALGEBRA}},
0437         volume = {114},
0438         year = {1988}
0439 }
0440 
0441 @article{PohlmeyerRehren:1988,
0442         author = {K. Pohlmeyer and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
0443         journal = {Commun. Math. Phys.},
0444         localfile = {1988 - Pohlmeyer, Rehren - THE INVARIANT CHARGES OF THE NAMBU-GOTO THEORY: THEIR GEOMETRIC ORIGIN AND THEIR COMPLETENESS.pdf},
0445         pages = {177},
0446         slaccitation = {\%\%CITATION = CMPHA,114,177\\;\%\%},
0447         title = {{THE INVARIANT CHARGES OF THE NAMBU-GOTO THEORY: THEIR GEOMETRIC ORIGIN AND THEIR COMPLETENESS}},
0448         volume = {114},
0449         year = {1988}
0450 }
0451 
0452 @article{BuchholzJunglas:1989,
0453         author = {D. Buchholz and P. Junglas},
0454         journal = {Commun. Math. Phys.},
0455         localfile = {1989 - Buchholz, Junglas - On the existence of equilibrium states in local quantum field theory.pdf},
0456         pages = {255--270},
0457         slaccitation = {\%\%CITATION = CMPHA,121,255\\;\%\%},
0458         title = {{ON THE EXISTENCE OF EQUILIBRIUM STATES IN LOCAL QUANTUM FIELD THEORY}},
0459         volume = {121},
0460         year = {1989}
0461 }
0462 
0463 @article{Borchers:1990,
0464         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
0465         journal = {Commun. Math. Phys.},
0466         localfile = {1990 - Borchers - Translation group and modular automorphisms for local regions.pdf},
0467         pages = {189--200},
0468         slaccitation = {\%\%CITATION = CMPHA,132,189\\;\%\%},
0469         title = {{Translation group and modular automorphisms for local regions}},
0470         volume = {132},
0471         year = {1990}
0472 }
0473 
0474 @article{BorchersYngvason:1990,
0475         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and J. Yngvason},
0476         doi = {10.1007/BF02104505},
0477         journal = {Commun. Math. Phys.},
0478         localfile = {1990 - Borchers, Yngvason - Positivity of Wightman functionals and the existence of local nets.pdf},
0479         pages = {607},
0480         slaccitation = {\%\%CITATION = CMPHA,127,607\\;\%\%},
0481         title = {{Positivity of Wightman functionals and the existence of local nets}},
0482         url = {http://projecteuclid.org/euclid.cmp/1104180223},
0483         volume = {127},
0484         year = {1990}
0485 }
0486 
0487 @article{Rehren:1990,
0488         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
0489         journal = {Commun. Math. Phys.},
0490         localfile = {1990 - Rehren - SPACE-TIME FIELDS AND EXCHANGE FIELDS.pdf},
0491         pages = {461--484},
0492         slaccitation = {\%\%CITATION = CMPHA,132,461\\;\%\%},
0493         title = {{SPACE-TIME FIELDS AND EXCHANGE FIELDS}},
0494         volume = {132},
0495         year = {1990}
0496 }
0497 
0498 @article{BorchersWollenberg:1991,
0499         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and M. Wollenberg},
0500         journal = {Commun. Math. Phys.},
0501         localfile = {1991 - Borchers, Wollenberg - On the relation between types of local algebras in different global representations.pdf},
0502         pages = {161--174},
0503         slaccitation = {\%\%CITATION = CMPHA,137,161\\;\%\%},
0504         title = {{On the relation between types of local algebras in different global representations}},
0505         volume = {137},
0506         year = {1991}
0507 }
0508 
0509 @article{KayWald:1991,
0510         author = {B. S. Kay and R. M. Wald},
0511         journal = {Phys. Rept.},
0512         localfile = {1991 - Kay, Wald - Theorems on the Uniqueness and Thermal Properties of Stationary, Nonsingular, Quasifree States on Space-Times with a Bifurcate Killing Horizon.pdf},
0513         pages = {49--136},
0514         slaccitation = {\%\%CITATION = PRPLC,207,49\\;\%\%},
0515         title = {{Theorems on the Uniqueness and Thermal Properties of Stationary, Nonsingular, Quasifree States on Space-Times with a Bifurcate Killing Horizon}},
0516         volume = {207},
0517         year = {1991}
0518 }
0519 
0520 @article{AshtekarIsham:1992,
0521         abstract = {Holonomy algebras arise naturally in the classical description of Yang-Mills fields and gravity, and it has been suggested, at a heuristic level, that they may also play an important role in a non-perturbative treatment of the quantum theory. The aim of this paper is to provide a mathematical basis for this proposal. The quantum holonomy algebra is constructed, and, in the case of real connections, given the structure of a certain C-star algebra. A proper representation theory is then provided using the Gel'fand spectral theory. A corollory of these general results is a precise formulation of the ``loop transform'' proposed by Rovelli and Smolin. Several explicit representations of the holonomy algebra are constructed. The general theory developed here implies that the domain space of quantum states can always be taken to be the space of maximal ideals of the C-star algebra. The structure of this space is investigated and it is shown how observables labelled by ``strips'' arise naturally.},
0522         author = {A. Ashtekar and C. J. Isham},
0523         eprint = {hep-th/9202053},
0524         journal = {Class. Quant. Grav.},
0525         localfile = {1992 - Ashtekar, Isham - Representations of the holonomy algebras of gravity and non-Abelian gauge theories.pdf},
0526         pages = {1433--1468},
0527         slaccitation = {\%\%CITATION = HEP-TH/9202053\\;\%\%},
0528         title = {{Representations of the holonomy algebras of gravity and nonAbelian gauge theories}},
0529         url = {http://arxiv.org/abs/hep-th/9202053},
0530         volume = {9},
0531         year = {1992}
0532 }
0533 
0534 @article{BuchholzWanzenberg:1992,
0535         author = {D. Buchholz and R. Wanzenberg},
0536         journal = {Commun. Math. Phys.},
0537         localfile = {1992 - Buchholz, Wanzenberg - The realm of the vacuum.pdf},
0538         pages = {577--590},
0539         slaccitation = {\%\%CITATION = CMPHA,143,577\\;\%\%},
0540         title = {{The Realm of the vacuum}},
0541         volume = {143},
0542         year = {1992}
0543 }
0544 
0545 @article{Kay:1993,
0546         author = {B. S. Kay},
0547         journal = {J. Math. Phys.},
0548         localfile = {1993 - Kay - Sufficient conditions for quasifree states and an improved uniqueness theorem for quantum fields on space-times with horizons.pdf},
0549         pages = {4519--4539},
0550         slaccitation = {\%\%CITATION = JMAPA,34,4519\\;\%\%},
0551         title = {{Sufficient conditions for quasifree states and an improved uniqueness theorem for quantum fields on space-times with horizons}},
0552         volume = {34},
0553         year = {1993}
0554 }
0555 
0556 @article{Rehren:1992,
0557         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
0558         journal = {Commun. Math. Phys.},
0559         localfile = {1992 - Rehren - Field operators for anyons and plektons.pdf},
0560         pages = {123--148},
0561         slaccitation = {\%\%CITATION = CMPHA,145,123\\;\%\%},
0562         title = {{Field operators for anyons and plektons}},
0563         volume = {145},
0564         year = {1992}
0565 }
0566 
0567 @article{Thirring:1992,
0568         author = {W. Thirring},
0569         localfile = {1992 - Thirring - Ergodic Properties in Quantum Systems.pdf},
0570         note = {UWTHPH-1992-6},
0571         title = {{Ergodic properties in quantum systems}},
0572         year = {1992}
0573 }
0574 
0575 @article{BrunettiGuidoLongo:1993,
0576         abstract = {Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories, i.e. the Tomita-Takesaki modular group associated with the von Neumann algebra of a wedge region and the vacuum vector concides with the evolution given by the rescaled pure Lorentz transformations preserving the wedge. A similar geometric description is valid for the algebras associated with double cones. Moreover essential duality holds on the Minkowski space $M$, and Haag duality for double cones holds provided the net of local algebras is extended to a pre-cosheaf on the superworld $\tilde M$, i.e. the universal covering of the Dirac-Weyl compactification of $M$. As a consequence a PCT symmetry exists for any algebraic conformal field theory in even space-time dimension. Analogous results hold for a Poincare covariant theory provided the modular groups corresponding to wedge algebras have the expected geometrical meaning and the split property is satisfied. In particular the Poincare representation is unique in this case.},
0577         author = {R. Brunetti and D. Guido and R. Longo},
0578         eprint = {funct-an/9302008},
0579         journal = {Commun. Math. Phys.},
0580         localfile = {1993 - Brunetti, Guido, Longo - Modular Structure and Duality in Conformal Quantum Field Theory.pdf},
0581         pages = {201--220},
0582         slaccitation = {\%\%CITATION = FUNCT-AN/9302008\\;\%\%},
0583         title = {{Modular structure and duality in conformal quantum field theory}},
0584         url = {http://arxiv.org/abs/funct-an/9302008},
0585         volume = {156},
0586         year = {1993}
0587 }
0588 
0589 @article{BuchholzDoplicherLongoRoberts:1993,
0590         author = {D. Buchholz and S. Doplicher and R. Longo and J. E. Roberts},
0591         journal = {Commun. Math. Phys.},
0592         localfile = {1993 - Buchholz, Doplicher, Longo, Roberts - Extensions of automorphisms and gauge symmetries.pdf},
0593         pages = {123--134},
0594         slaccitation = {\%\%CITATION = CMPHA,155,123\\;\%\%},
0595         title = {{Extensions of automorphisms and gauge symmetries}},
0596         volume = {155},
0597         year = {1993}
0598 }
0599 
0600 @article{FringMussardoSimonetti:1993,
0601         abstract = {We derive the recursive equations for the form factors of the local hermitian operators in the Bullough-Dodd model. At the self-dual point of the theory, the form factors of the fundamental field of the Bullough-Dodd model are equal to those of the fundamental field of the Sinh-Gordon model at a specific value of the coupling constant.},
0602         author = {A. Fring and G. Mussardo and P. Simonetti},
0603         eprint = {hep-th/9303108},
0604         journal = {Phys. Lett.},
0605         localfile = {1993 - Fring, Mussardo, Simonetti - Form Factors of the Elementary Field in the Bullough-Dodd Model.pdf},
0606         pages = {83--90},
0607         slaccitation = {\%\%CITATION = HEP-TH/9303108\\;\%\%},
0608         title = {{Form-factors of the elementary field in the Bullough-Dodd model}},
0609         url = {http://arxiv.org/abs/hep-th/9303108},
0610         volume = {B307},
0611         year = {1993}
0612 }
0613 
0614 @article{BuchholzYngvason:1994,
0615         abstract = {A repeatedly discussed gedanken experiment, proposed by Fermi to check Einstein causality, is reconsidered. It is shown that, contrary to a recent statement made by Hegerfeldt, there appears no causality paradoxon in a proper theoretical description of the experiment.},
0616         author = {D. Buchholz and J. Yngvason},
0617         eprint = {hep-th/9403027},
0618         journal = {Phys. Rev. Lett.},
0619         localfile = {1994 - Buchholz, Yngvason - There are no causality problems for Fermis Two Atom System.pdf},
0620         pages = {613--616},
0621         slaccitation = {\%\%CITATION = HEP-TH/9403027\\;\%\%},
0622         title = {{There are no causality problems for Fermi's two atom system}},
0623         url = {http://arxiv.org/abs/hep-th/9403027},
0624         volume = {73},
0625         year = {1994}
0626 }
0627 
0628 @article{DoplicherFredenhagenRoberts:1995,
0629         abstract = {We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation relations exactly implement our uncertainty relations. We outline the definition of free fields and interactions over QST and take the first steps to adapting the usual perturbation theory. The quantum nature of the underlying spacetime replaces a local interaction by a specific nonlocal effective interaction in the ordinary Minkowski space. A detailed study of interacting QFT and of the smoothing of ultraviolet divergences is deferred to a subsequent paper. In the classical limit where the Planck length goes to zero, our Quantum Spacetime reduces to the ordinary Minkowski space times a two component space whose components are homeomorphic to the tangent bundle TS^2 of the 2-sphere. The relations with Connes' theory of the standard model will be studied elsewhere.},
0630         author = {S. Doplicher and K. Fredenhagen and J. E. Roberts},
0631         eprint = {hep-th/0303037},
0632         journal = {Commun. Math. Phys.},
0633         localfile = {1994 - Doplicher, Fredenhagen, Roberts - The Quantum Structure of Spacetime at the Planck Scale and Quantum Fields.pdf},
0634         pages = {187--220},
0635         slaccitation = {\%\%CITATION = HEP-TH/0303037\\;\%\%},
0636         title = {{The Quantum structure of space-time at the {P}lanck scale and quantum fields}},
0637         url = {http://arxiv.org/abs/hep-th/0303037},
0638         volume = {172},
0639         year = {1995}
0640 }
0641 
0642 @article{Lashkevich:1994,
0643         abstract = {It is known that 2D field theories admit several sectors of mutually local fields so as two fields from different sectors are mutually nonlocal. We show that any one-partical integrable model with ${\bf Z}_2$ symmetry contains three sectors: bosonic, fermionic and `disorder' one. We generalize the form factor axioms to fermionic and `disorder' sectors. For the particular case of the sinh-Gordon model we obtain several form factors in these sectors.},
0644         author = {M. Yu. Lashkevich},
0645         eprint = {hep-th/9406118},
0646         localfile = {1994 - Lashkevich - Sectors of mutually local fields in integrable models of quantum field theory.pdf},
0647         slaccitation = {\%\%CITATION = HEP-TH/9406118\\;\%\%},
0648         title = {{Sectors of mutually local fields in integrable models of quantum field theory}},
0649         url = {http://arxiv.org/abs/hep-th/9406118},
0650         year = {1994}
0651 }
0652 
0653 @article{Smirnov:1994,
0654         abstract = {Some mistaken reasonings at the end of the paper omitted.},
0655         author = {F. A. Smirnov},
0656         eprint = {hep-th/9312039},
0657         journal = {Int. J. Mod. Phys.},
0658         localfile = {1994 - Smirnov - A New set of exact form-factors.pdf},
0659         pages = {5121--5144},
0660         slaccitation = {\%\%CITATION = HEP-TH/9312039\\;\%\%},
0661         title = {{A New set of exact form-factors}},
0662         url = {http://arxiv.org/abs/hep-th/9312039},
0663         volume = {A9},
0664         year = {1994}
0665 }
0666 
0667 @article{Verch:1994,
0668         author = {R. Verch},
0669         journal = {Commun. Math. Phys.},
0670         localfile = {1994 - Verch - Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved spacetime.pdf},
0671         pages = {507--536},
0672         slaccitation = {\%\%CITATION = CMPHA,160,507\\;\%\%},
0673         title = {{Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved space-time}},
0674         volume = {160},
0675         year = {1994}
0676 }
0677 
0678 @article{Borchers:1995,
0679         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
0680         journal = {Annales Poincare Phys. Theor.},
0681         localfile = {1995 - Borchers - On the use of modular groups in quantum field theory.pdf},
0682         pages = {331--382},
0683         slaccitation = {\%\%CITATION = AHPAA,63,331\\;\%\%},
0684         title = {{On the use of modular groups in quantum field theory}},
0685         volume = {63},
0686         year = {1995}
0687 }
0688 
0689 @article{LiguoriMintchev:1995-1,
0690         abstract = {We develop a rigorous framework for constructing Fock representations of quantum fields obeying generalized statistics associated with certain solutions of the spectral quantum Yang-Baxter equation. The main features of these representations are investigated. Various aspects of the underlying mathematical structure are illustrated by means of explicit examples.},
0691         author = {A. Liguori and M. Mintchev},
0692         eprint = {hep-th/9403039},
0693         journal = {Commun. Math. Phys.},
0694         localfile = {1995 - Liguori, Mintchev - Fock representations of quantum fields with generalized statistics.pdf},
0695         pages = {635--652},
0696         slaccitation = {\%\%CITATION = HEP-TH/9403039\\;\%\%},
0697         title = {{Fock representations of quantum fields with generalized statistics}},
0698         url = {http://arxiv.org/abs/hep-th/9403039},
0699         volume = {169},
0700         year = {1995}
0701 }
0702 
0703 @article{LiguoriMintchevRossi:1995,
0704         author = {A. Liguori and M. Mintchev and M. Rossi},
0705         journal = {Lett. Math. Phys.},
0706         localfile = {1995 - Liguori, Mintchev, Rossi - Unitary Group Representations in Fock Spaces with Generalized Exchange Properties.pdf},
0707         pages = {163--177},
0708         slaccitation = {\%\%CITATION = LMPHD,35,163\\;\%\%},
0709         title = {{Unitary group representations in Fock spaces with generalized exchange properties}},
0710         volume = {35},
0711         year = {1995}
0712 }
0713 
0714 @article{FlorigSummers:1997,
0715         author = {M. Florig and S. J. Summers},
0716         journal = {J. Math. Phys.},
0717         localfile = {1996 - Florig, Summers - On the statistical independence of algebras of observables.pdf},
0718         pages = {1318--1328},
0719         slaccitation = {\%\%CITATION = JMAPA,38,1318\\;\%\%},
0720         title = {{On the statistical independence of algebras of observables}},
0721         volume = {38},
0722         year = {1997}
0723 }
0724 
0725 @article{Jr:1996,
0726         abstract = {Starting from a conformal Haag-Kastler net in 1+1 dimensions, Wightman functions are constructed.},
0727         author = {M. J{\"{o}}r{\ss}},
0728         eprint = {hep-th/9609020},
0729         localfile = {1996 - Jorss - From conformal Haag-Kastler nets to Wightman functions.pdf},
0730         slaccitation = {\%\%CITATION = HEP-TH/9609020\\;\%\%},
0731         title = {{From conformal Haag-Kastler nets to Wightman functions}},
0732         url = {http://arxiv.org/abs/hep-th/9609020},
0733         year = {1996}
0734 }
0735 
0736 @article{Rehren:1996,
0737         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
0738         journal = {Commun. Math. Phys.},
0739         localfile = {1996 - Rehren - Comments on a recent solution to Wightman's axioms.pdf},
0740         pages = {453--466},
0741         slaccitation = {\%\%CITATION = CMPHA,178,453\\;\%\%},
0742         title = {{Comments on a recent solution to Wightman's axioms}},
0743         volume = {178},
0744         year = {1996}
0745 }
0746 
0747 @article{RehrenStanevTodorov:1995,
0748         abstract = {Pairs ${\aa}\subset \bb$ of local quantum field theories are studied, where ${\aa}$ is a chiral conformal \qft and $\bb$ is a local extension, either chiral or two-dimensional. The local correlation functions of fields from $\bb$ have an expansion with respect to ${\aa}$ into \cfb s, which are non-local in general. Two methods of computing characteristic invariant ratios of structure constants in these expansions are compared: $(a)$ by constructing the monodromy \rep of the braid group in the space of solutions of the Knizhnik-Zamolodchikov differential equation, and $(b)$ by an analysis of the local subfactors associated with the extension with methods from operator algebra (Jones theory) and algebraic quantum field theory. Both approaches apply also to the reverse problem: the characterization and (in principle) classification of local extensions of a given theory.},
0749         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren and Y. S. Stanev and I. T. Todorov},
0750         eprint = {hep-th/9409165},
0751         journal = {Commun. Math. Phys.},
0752         localfile = {1995 - Rehren, Stanev, TodorovIvan T - Characterizing invariants for local extensions of current algebras.pdf},
0753         pages = {605--634},
0754         slaccitation = {\%\%CITATION = HEP-TH/9409165\\;\%\%},
0755         title = {{Characterizing invariants for local extensions of current algebras}},
0756         url = {http://arxiv.org/abs/hep-th/9409165},
0757         volume = {174},
0758         year = {1995}
0759 }
0760 
0761 @article{Schroer:1997-2,
0762         abstract = {We present illustrations which show the usefulness of algebraic QFT. In particular in low-dimensional QFT, when Lagrangian quantization does not exist or is useless (e.g. in chiral conformal theories), the algebraic method is beginning to reveal its strength.},
0763         author = {B. Schroer},
0764         eprint = {hep-th/9608083},
0765         journal = {Annals Phys.},
0766         localfile = {1997 - Schroer - Motivations and physical aims of algebraic QFT.pdf},
0767         pages = {270--304},
0768         slaccitation = {\%\%CITATION = HEP-TH/9608083\\;\%\%},
0769         title = {{Motivations and physical aims of algebraic QFT}},
0770         url = {http://arxiv.org/abs/hep-th/9608083},
0771         volume = {255},
0772         year = {1997}
0773 }
0774 
0775 @article{Schumann:1996,
0776         author = {R. Schumann},
0777         journal = {Lett. Math. Phys.},
0778         localfile = {1996 - Schumann - Operator Ideals and the Statistical Independence in Quantum Field Theory.pdf},
0779         pages = {249--271},
0780         slaccitation = {\%\%CITATION = LMPHD,37,249\\;\%\%},
0781         title = {{Operator ideals and the statistical independence in quantum field theory}},
0782         volume = {37},
0783         year = {1996}
0784 }
0785 
0786 @article{Yngvason:1996,
0787         author = {J. Yngvason},
0788         journal = {Annales Poincare Phys. Theor.},
0789         localfile = {1996 - Yngvason - Tomita Conjugations and Transitivity of Locality.pdf},
0790         pages = {395--408},
0791         slaccitation = {\%\%CITATION = AHPAA,64,395\\;\%\%},
0792         title = {{Tomita conjugations and transitivity of locality}},
0793         volume = {64},
0794         year = {1996}
0795 }
0796 
0797 @article{LiguoriMintchevRossi:1997,
0798         author = {A. Liguori and M. Mintchev and M. Rossi},
0799         journal = {J. Math. Phys.},
0800         localfile = {1997 - Liguori, Mintchev, Rossi - Fock representations of exchange algebras with involution.pdf},
0801         pages = {2888--2898},
0802         slaccitation = {\%\%CITATION = JMAPA,38,2888\\;\%\%},
0803         title = {{Fock representations of exchange algebras with involution}},
0804         volume = {38},
0805         year = {1997}
0806 }
0807 
0808 @article{Niedermaier:1998,
0809         abstract = {A derivation of the cyclic form factor equation from quantum field theoretical principles is given; form factors being the matrix elements of a field operator between scattering states. The scattering states are constructed from Haag-Ruelle type interpolating fields with support in a `comoving' Rindler spacetime. The cyclic form factor equation then arises from the KMS property of the modular operators Delta associated with the field algebras of these Rindler wedges. The derivation in particular shows that the equation holds in any massive 1+1 dim. relativistic QFT, regardless of its integrability.},
0810         author = {M. R. Niedermaier},
0811         eprint = {hep-th/9706172},
0812         journal = {Commun. Math. Phys.},
0813         localfile = {1997 - Niedermaier - A Derivation of the Cyclic Form Factor Equation.pdf},
0814         pages = {411--428},
0815         slaccitation = {\%\%CITATION = HEP-TH/9706172\\;\%\%},
0816         title = {{A derivation of the cyclic form factor equation}},
0817         url = {http://arxiv.org/abs/hep-th/9706172},
0818         volume = {196},
0819         year = {1998}
0820 }
0821 
0822 @article{Rehren:1998,
0823         abstract = {The statistics of soliton sectors of massive 2D field theories is analysed. In the soliton field algebra, the non-local commutation relations are determined and Weak Locality, Spin-Statistics and CPT theorems are proven. These theorems depart from their usual appearance due to the broken symmetry connecting the inequivalent vacua. An interpretation in terms of modular theory is given. For the neutral subalgebra, the theorems hold in the familiar form, and Twisted Locality is derived.},
0824         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
0825         eprint = {hep-th/9711085},
0826         journal = {Lett. Math. Phys.},
0827         localfile = {1998 - Rehren - Spin statistics and CPT for solitons.pdf},
0828         pages = {95--110},
0829         slaccitation = {\%\%CITATION = HEP-TH/9711085\\;\%\%},
0830         title = {{Spin statistics and CPT for solitons}},
0831         url = {http://arxiv.org/abs/hep-th/9711085},
0832         volume = {46},
0833         year = {1998}
0834 }
0835 
0836 @article{ThomasWichmann:1997,
0837         author = {L. J. Thomas and E. H. Wichmann},
0838         doi = {10.1063/1.531954},
0839         journal = {J. Math. Phys.},
0840         localfile = {1997 - Thomas, Wichmann - On the Causal Structure of Minkowski Spacetime.pdf},
0841         pages = {5044--5086},
0842         slaccitation = {\%\%CITATION = JMAPA,38,5044\\;\%\%},
0843         title = {{On the causal structure of {M}inkowski space-time}},
0844         volume = {38},
0845         year = {1997}
0846 }
0847 
0848 @article{BuchholzDreyerFlorigSummers:2000,
0849         abstract = {A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides these groups with projective representations. Under suitable additional conditions, these groups induce groups of point transformations on these space-times, which may be interpreted as symmetry groups. The consequences of this condition are studied in detail in application to two concrete space-times -- four-dimensional Minkowski and three-dimensional de Sitter spaces -- for which it is shown how this condition characterizes the states invariant under the respective isometry group. An intriguing new algebraic characterization of vacuum states is given. In addition, the logical relations between the condition proposed in this paper and the condition of modular covariance, widely used in the literature, are completely illuminated.},
0850         author = {D. Buchholz and O. Dreyer and M. Florig and S. J. Summers},
0851         eprint = {math-ph/9805026},
0852         journal = {Rev. Math. Phys.},
0853         localfile = {1998 - Buchholz, Dreyer, Florig, Summers - Geometric modular action and spacetime symmetry groups.pdf},
0854         pages = {475--560},
0855         slaccitation = {\%\%CITATION = MATH-PH/9805026\\;\%\%},
0856         title = {{Geometric modular action and spacetime symmetry groups}},
0857         url = {http://arxiv.org/abs/math-ph/9805026},
0858         volume = {12},
0859         year = {2000}
0860 }
0861 
0862 @article{FlorigSummers:2000,
0863         abstract = {We construct a new class of representations of the canonical commutation relations, which generalizes previously known classes. We perturb the infinitesimal generator of the initial Fock representation (i.e. the free quantum field) by a function of the field which is square-integrable with respect to the associated Gaussian measure. We characterize which such perturbations lead to representations of the canonical commutation relations. We provide conditions entailing the irreducibility of such representations, show explicitly that our class of representations subsumes previously studied classes, and give necessary and sufficient conditions for our representations to be unitarily equivalent, resp. quasi-equivalent, with Fock, coherent or quasifree representations.},
0864         author = {M. Florig and S. J. Summers},
0865         eprint = {math-ph/0006011},
0866         journal = {Proc. Lond. Math. Soc.},
0867         localfile = {2000 - Florig, Summers - Further representations of the canonical commutation relations.pdf},
0868         pages = {451--490},
0869         slaccitation = {\%\%CITATION = MATH-PH/0006011\\;\%\%},
0870         title = {{Further representations of the canonical commutation relations}},
0871         url = {http://arxiv.org/abs/math-ph/0006011},
0872         volume = {80},
0873         year = {2000}
0874 }
0875 
0876 @article{SchroerWiesbrock:2000-1,
0877         abstract = {We extend the previously introduced constructive modular method to nonperturbative QFT. In particular the relevance of the concept of ``quantum localization'' (via intersection of algebras) versus classical locality (via support properties of test functions) is explained in detail, the wedge algebras are constructed rigorously and the formal aspects of double cone algebras for d=1+1 factorizing theories are determined. The well-known on-shell crossing symmetry of the S-Matrix and of formfactors (cyclicity relation) in such theories is intimately related to the KMS properties of new quantum-local PFG (one-particle polarization-free generators) of these wedge algebras. These generators are ``on-shell'' and their Fourier transforms turn out to fulfill the Zamolodchikov-Faddeev algebra. As the wedge algebras contain the crossing symmetry informations, the double cone algebras reveal the particle content of fields. Modular theory associates with this double cone algebra two very useful chiral conformal quantum field theories which are the algebraic versions of the light ray algebras.},
0878         author = {B. Schroer and H.W. Wiesbrock},
0879         eprint = {hep-th/9812251},
0880         journal = {Rev. Math. Phys.},
0881         localfile = {1998 - Schroer, Wiesbrock - Modular constructions of quantum field theories with interactions.pdf},
0882         pages = {301--326},
0883         slaccitation = {\%\%CITATION = HEP-TH/9812251\\;\%\%},
0884         title = {{Modular constructions of quantum field theories with interactions}},
0885         url = {http://arxiv.org/abs/hep-th/9812251},
0886         volume = {12},
0887         year = {2000}
0888 }
0889 
0890 @article{ThomasWichmann:1998,
0891         author = {L. J. Thomas and E. H. Wichmann},
0892         journal = {J. Math. Phys.},
0893         localfile = {1998 - Thomas, Wichmann - Standard Forms of local nets in quantum field theory.pdf},
0894         pages = {2643--2681},
0895         slaccitation = {\%\%CITATION = JMAPA,39,2643\\;\%\%},
0896         title = {{Standard forms of local nets in quantum field theory}},
0897         volume = {39},
0898         year = {1998}
0899 }
0900 
0901 @article{BabujianKarowski:1999,
0902         abstract = {Using the methods of the form factor program exact expressions of all matrix elements are obtained for several operators of the quantum sine Gordon model: all powers of the fundamental bose field, general exponentials of it, the energy momentum tensor and all higher currents. It is found that the quantum sine-Gordon field equation holds with an exact relation between the bare mass and the renormalized mass. Also a relation for the trace of the energy momentum is obtained. The eigenvalue problem for all higher conserved charges is solved. All results are compared with Feynman graph expansions and full agreement is found.},
0903         author = {H. M. Babujian and M. Karowski},
0904         eprint = {hep-th/9909153},
0905         journal = {Phys. Lett.},
0906         localfile = {1999 - Babujian, Karowski - The Exact Quantum Sine-Gordon Field Equation and Other Non-Perturbative Results.pdf},
0907         pages = {53--57},
0908         slaccitation = {\%\%CITATION = HEP-TH/9909153\\;\%\%},
0909         title = {{The exact quantum sine-Gordon field equation and other non- perturbative results}},
0910         url = {http://arxiv.org/abs/hep-th/9909153},
0911         volume = {B471},
0912         year = {1999}
0913 }
0914 
0915 @article{Fewster:2000,
0916         abstract = {Worldline quantum inequalities provide lower bounds on weighted averages of the renormalised energy density of a quantum field along the worldline of an observer. In the context of real, linear scalar field theory on an arbitrary globally hyperbolic spacetime, we establish a worldline quantum inequality on the normal ordered energy density, valid for arbitrary smooth timelike trajectories of the observer, arbitrary smooth compactly supported weight functions and arbitrary Hadamard quantum states. Normal ordering is performed relative to an arbitrary choice of Hadamard reference state. The inequality obtained generalises a previous result derived for static trajectories in a static spacetime. The underlying argument is straightforward and is made rigorous using the techniques of microlocal analysis. In particular, an important role is played by the characterisation of Hadamard states in terms of the microlocal spectral condition. We also give a compact form of our result for stationary trajectories in a stationary spacetime.},
0917         author = {C. J. Fewster},
0918         eprint = {gr-qc/9910060},
0919         journal = {Class. Quant. Grav.},
0920         localfile = {2000 - Fewster - A general worldline quantum inequality.pdf},
0921         pages = {1897--1911},
0922         slaccitation = {\%\%CITATION = GR-QC/9910060\\;\%\%},
0923         title = {{A general worldline quantum inequality}},
0924         url = {http://arxiv.org/abs/gr-qc/9910060},
0925         volume = {17},
0926         year = {2000}
0927 }
0928 
0929 @article{FewsterTeo:1999,
0930         abstract = {Certain exotic phenomena in general relativity, such as backward time travel, appear to require the presence of matter with negative energy. While quantum fields are a possible source of negative energy densities, there are lower bounds - known as quantum inequalities - that constrain their duration and magnitude. In this paper, we derive new quantum inequalities for scalar fields in static space-times, as measured by static observers with a choice of sampling function. Unlike those previously derived by Pfenning and Ford, our results do not assume any specific sampling function. We then calculate these bounds in static three- and four-dimensional Robertson-Walker universes, the de Sitter universe, and the Schwarzschild black hole. In each case, the new inequality is stronger than that of Pfenning and Ford for their particular choice of sampling function.},
0931         author = {C. J. Fewster and E. Teo},
0932         eprint = {gr-qc/9812032},
0933         journal = {Phys. Rev.},
0934         localfile = {1999 - Fewster, Teo - Bounds on negative energy densities in static space-times.pdf},
0935         pages = {104016},
0936         slaccitation = {\%\%CITATION = GR-QC/9812032\\;\%\%},
0937         title = {{Bounds on negative energy densities in static space-times}},
0938         url = {http://arxiv.org/abs/gr-qc/9812032},
0939         volume = {D59},
0940         year = {1999}
0941 }
0942 
0943 @article{GaierYngvason:2000,
0944         author = {J. Gaier and J. Yngvason},
0945         journal = {J. Math. Phys.},
0946         localfile = {1999 - Gaier, Yngvason - Geometric Modular Action, Wedge Duality and Lorentz Covariance are Equivalent for Generalized Free Fields.pdf},
0947         pages = {5910--5919},
0948         slaccitation = {\%\%CITATION = JMAPA,41,5910\\;\%\%},
0949         title = {{Geometric modular action, wedge duality, and Lorentz covariance are equivalent for generalized free fields}},
0950         volume = {41},
0951         year = {2000}
0952 }
0953 
0954 @article{GuidoLongoRobertsVerch:2001,
0955         abstract = {The first part of this paper extends the Doplicher-Haag-Roberts theory of superselection sectors to quantum field theory on arbitrary globally hyperbolic spacetimes. The statistics of a superselection sector may be defined as in flat spacetime and each charge has a conjugate charge when the spacetime possesses non-compact Cauchy surfaces. In this case, the field net and the gauge group can be constructed as in Minkowski spacetime. The second part of this paper derives spin-statistics theorems on spacetimes with appropriate symmetries. Two situations are considered: First, if the spacetime has a bifurcate Killing horizon, as is the case in the presence of black holes, then restricting the observables to the Killing horizon together with modular covariance for the Killing flow yields a conformally covariant quantum field theory on the circle and a conformal spin-statistics theorem for charged sectors localizable on the Killing horizon. Secondly, if the spacetime has a rotation and PT symmetry like the Schwarzschild-Kruskal black holes, geometric modular action of the rotational symmetry leads to a spin-statistics theorem for charged covariant sectors where the spin is defined via the SU(2)-covering of the spatial rotation group SO(3).},
0956         author = {D. Guido and R. Longo and J. E. Roberts and R. Verch},
0957         doi = {10.1142/S0129055X01000557},
0958         eprint = {math-ph/9906019},
0959         journal = {Rev. Math. Phys.},
0960         localfile = {1999 - Guido, Longo, Roberts, Verch - Charged sectors, spin and statistics in quantum field theory on curved spacetimes.pdf},
0961         pages = {125--198},
0962         slaccitation = {\%\%CITATION = MATH-PH/9906019\\;\%\%},
0963         title = {{Charged sectors, spin and statistics in quantum field theory on curved spacetimes}},
0964         url = {http://arxiv.org/abs/math-ph/9906019},
0965         volume = {13},
0966         year = {2001}
0967 }
0968 
0969 @article{Rainer:1999,
0970         abstract = {We investigate up to which extend the kinematic setting of loop quantum gravity can be fit into a diffeomorphism invariant setting of algebraic QFT generalizing the Haag-Kastler setting of Wightman type QFT. The net of local (Weyl-)algebras resulting from a spin network state of quantum geometry immediately accommodates isotony and diffeomorphism covariance, and formulation of causality becomes possible via of diffeomorphism invariant foliations of the underlying manifold by cones. On a spatial horizon, quantum geometry becomes asymptotically a genuine QFT with infinitely many degrees of freedom, if the cylinder functions' supporting graphs intersect the inner boundary spheres in an infinite number of punctures.},
0971         author = {M. Rainer},
0972         eprint = {gr-qc/9912011},
0973         localfile = {1999 - Rainer - Is loop quantum gravity a QFT?.pdf},
0974         slaccitation = {\%\%CITATION = GR-QC/9912011\\;\%\%},
0975         title = {{Is loop quantum gravity a QFT?}},
0976         url = {http://arxiv.org/abs/gr-qc/9912011},
0977         year = {1999}
0978 }
0979 
0980 @article{Borchers:2000,
0981         abstract = {In the book of Haag [Ha92] about local quantum eld theory the main results are obtained by the older methods of C- and W-algebra theory. A great advance, especially in the theory of W-algebras, is due to Tomita's discovery of the theory of modular Hilbert algebras [To67]. Because of the abstract nature of the underlying concepts, this theory became (except for some sporadic results) a technique for quantum eld theory only in the beginning of the nineties. In this review the results obtained up to this point will be collected and some problems for the future will be discussed at the end. In the rst section the technical tools will be presented. Then in the second section two concepts, the half-sided translations and the half-sided modular inclusions, will be explained. These concepts have revolutionized the handling of quantum eld theory. Examples for which the modular groups are explicitly known are presented in the third section. One of the important results of the new theory is the proof of the PCT-theorem in the theory of local observables. Questions connected with the proof are discussed in section four. Section ve deals with the structure of local algebras and with questions connected with symmetry groups. In section six a theory of tensor product decompositions will be presented. In the last section problems closely connected with the modular theory and should be treated in the future will be discussed.},
0982         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
0983         journal = {J. Math. Phys.},
0984         localfile = {2000 - Borchers - On Revolutionizing Quantum Field Theory.pdf},
0985         pages = {3604--3673},
0986         slaccitation = {\%\%CITATION = JMAPA,41,3604\\;\%\%},
0987         title = {{On revolutionizing quantum field theory with Tomita's modular theory}},
0988         volume = {41},
0989         year = {2000}
0990 }
0991 
0992 @article{BuchholzDoplicherMorchioRobertsStrocchi:2001,
0993         abstract = {The classical Maxwell-Dirac and Maxwell-Klein-Gordon theories admit solutions of the field equations where the corresponding electric current vanishes in the causal complement of some bounded region of Minkowski space. This poses the interesting question of whether states with a similarly well localized charge density also exist in quantum electrodynamics. For a large family of charged states, the dominant quantum corrections at spacelike infinity to the expectation values of local observables are computed. It turns out that certain moments of the charge density decrease no faster than the Coulomb field in spacelike directions. In contrast to the classical theory, it is therefore impossible to define the electric charge support of these states in a meaningful way.},
0994         author = {D. Buchholz and S. Doplicher and G. Morchio and J. E. Roberts and F. Strocchi},
0995         eprint = {hep-th/0011015},
0996         journal = {Ann. Phys.},
0997         localfile = {2000 - Buchholz, Doplicher, Morchio, Roberts, Strocchi - Quantum Delocalization of the Electric Charge.pdf},
0998         pages = {53--66},
0999         slaccitation = {\%\%CITATION = HEP-TH/0011015\\;\%\%},
1000         title = {{Quantum delocalization of the electric charge}},
1001         url = {http://arxiv.org/abs/hep-th/0011015},
1002         volume = {290},
1003         year = {2001}
1004 }
1005 
1006 @article{BuchholzMundSummers:2001,
1007         abstract = {A novel method of transplanting algebras of observables from de Sitter space to a large class of Robertson-Walker space-times is exhibited. It allows one to establish the existence of an abundance of local nets on these spaces which comply with a recently proposed condition of geometric modular action. The corresponding modular symmetry groups appearing in these examples also satisfy a condition of modular stability, which has been suggested as a substitute for the requirement of positivity of the energy in Minkowski space. Moreover, they exemplify the conjecture that the modular symmetry groups are generically larger than the isometry and conformal groups of the underlying space-times.},
1008         author = {D. Buchholz and J. Mund and S. J. Summers},
1009         eprint = {hep-th/0011237},
1010         journal = {Fields Inst. Commun.},
1011         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
1012         localfile = {2000 - Buchholz, Mund, Summers - Transplantation of Local Nets and Geometric Modular Action on Robertson-Walker Space-Times.pdf},
1013         pages = {65--81},
1014         pdf = {http://arxiv.org/pdf/hep-th/0011237},
1015         slaccitation = {\%\%CITATION = HEP-TH/0011237\\;\%\%},
1016         title = {{Transplantation of Local Nets and Geometric Modular Action on Robertson-Walker Space-Times}},
1017         url = {http://arxiv.org/abs/hep-th/0011237},
1018         v1descr = {Mon, 27 Nov 2000 14:07:33 GMT (23kb)},
1019         v2descr = {Fri, 15 Dec 2000 13:00:27 GMT (23kb)},
1020         volume = {30},
1021         year = {2001}
1022 }
1023 
1024 @article{Fleischhack:2000,
1025         abstract = {Different versions for defining Ashtekar's generalized connections are investigated depending on the chosen smoothness category for the paths and graphs -- the label set for the projective limit. Our definition covers the analytic case as well as the case of webs. Then the orbit types of the generalized connections are determined for compact structure groups. The stabilizer of a connection is homeomorphic to the holonomy centralizer, i.e. the centralizer of its holonomy group, and the homeomorphism class of the gauge orbit is completely determined by the holonomy centralizer. Furthermore, the stabilizers of two connections are conjugate in the gauge group if and only if their holonomy centralizers are conjugate in the structure group. Finally, the gauge orbit type of a connection is defined to be the conjugacy class of its holonomy centralizer equivalently to the standard definition via stabilizers.},
1026         author = {C. Fleischhack},
1027         eprint = {math-ph/0001006},
1028         journal = {Commun. Math. Phys.},
1029         localfile = {2000 - Fleischhack - Gauge Orbit Types for Generalized Connections.pdf},
1030         pages = {607--649},
1031         slaccitation = {\%\%CITATION = MATH-PH/0001006\\;\%\%},
1032         title = {{Gauge Orbit Types for Generalized Connections}},
1033         url = {http://arxiv.org/abs/math-ph/0001006},
1034         volume = {214},
1035         year = {2000}
1036 }
1037 
1038 @article{Fleischhack:2000-1,
1039         abstract = {Properties of the space $\Ab$ of generalized connections in the Ashtekar framework are investigated. First a construction method for new connections is given. The new parallel transports differ from the original ones only along paths that pass an initial segment of a fixed path. This is closely related to a new notion of path independence. Although we do not restrict ourselves to the immersive smooth or analytical case, any finite set of paths depends on a finite set of independent paths, a so-called hyph. This generalizes the well-known directedness of the set of smooth webs and that of analytical graphs, respectively. Due to these propositions, on the one hand, the projections from $\Ab$ to the lattice gauge theory are surjective and open. On the other hand, an induced Haar measure can be defined for every compact structure group irrespective of the used smoothness category for the paths.},
1040         author = {C. Fleischhack},
1041         eprint = {math-ph/0001007},
1042         localfile = {2000 - Fleischhack - Hyphs and the Ashtekar-Lewandowski measure.pdf},
1043         slaccitation = {\%\%CITATION = MATH-PH/0001007\\;\%\%},
1044         title = {{Hyphs and the Ashtekar-Lewandowski measure}},
1045         url = {http://arxiv.org/abs/math-ph/0001007},
1046         year = {2000}
1047 }
1048 
1049 @article{Fleischhack:2000-2,
1050         abstract = {The action of Ashtekar's generalized gauge group $\Gb$ on the space $\Ab$ of generalized connections is investigated for compact structure groups $\LG$. First a stratum is defined to be the set of all connections of one and the same gauge orbit type, i.e. the conjugacy class of the centralizer of the holonomy group. Then a slice theorem is proven on $\Ab$. This yields the openness of the strata. Afterwards, a denseness theorem is proven for the strata. Hence, $\Ab$ is topologically regularly stratified by $\Gb$. These results coincide with those of Kondracki and Rogulski for Sobolev connections. As a by-product, we prove that the set of all gauge orbit types equals the set of all (conjugacy classes of) Howe subgroups of $\LG$. Finally, we show that the set of all gauge orbits with maximal type has the full induced Haar measure 1.},
1051         author = {C. Fleischhack},
1052         eprint = {math-ph/0001008},
1053         localfile = {2000 - Fleischhack - Stratification of the Generalized Gauge Orbit Space.pdf},
1054         slaccitation = {\%\%CITATION = MATH-PH/0001008\\;\%\%},
1055         title = {{Stratification of the Generalized Gauge Orbit Space}},
1056         url = {http://arxiv.org/abs/math-ph/0001008},
1057         year = {2000}
1058 }
1059 
1060 @article{Oeckl:2000,
1061         abstract = {We show that there is a duality exchanging noncommutativity and non-trivial statistics for quantum field theory on R^d. Employing methods of quantum groups, we observe that ordinary and noncommutative R^d are related by twisting. We extend the twist to an equivalence for quantum field theory using the framework of braided quantum field theory. The twist exchanges both commutativity with noncommutativity and ordinary with non-trivial statistics. The same holds for the noncommutative torus.},
1062         author = {R. Oeckl},
1063         eprint = {hep-th/0003018},
1064         journal = {Nucl. Phys.},
1065         localfile = {2000 - Oeckl - Untwisting noncommutative R**d and the equivalence of quantum field theories.pdf},
1066         pages = {559--574},
1067         slaccitation = {\%\%CITATION = HEP-TH/0003018\\;\%\%},
1068         title = {{Untwisting noncommutative R**d and the equivalence of quantum field theories}},
1069         url = {http://arxiv.org/abs/hep-th/0003018},
1070         volume = {B581},
1071         year = {2000}
1072 }
1073 
1074 @article{Ramacher:2000,
1075         author = {P. Ramacher},
1076         journal = {J. Math. Phys.},
1077         localfile = {2000 - Ramacher - Modular localization of elementary systems in the theory of Wigner.pdf},
1078         pages = {6079--6089},
1079         slaccitation = {\%\%CITATION = JMAPA,41,6079\\;\%\%},
1080         title = {{Modular localization of elementary systems in the theory of Wigner}},
1081         volume = {41},
1082         year = {2000}
1083 }
1084 
1085 @article{DtschFredenhagen:2001-1,
1086         abstract = {The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system ${\cal A}^{(n)}$ of observables ``up to $n$ loops'' where ${\cal A}^{(0)}$ is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of Green's functions.},
1087         author = {M. D{\"{u}}tsch and K. Fredenhagen},
1088         eprint = {hep-th/0001129},
1089         journal = {Commun. Math. Phys.},
1090         localfile = {2001 - D\"{u}tsch, Fedenhagen - Perturbative Algebraic Field Theory, and Deformation Quantization.pdf},
1091         pages = {5--30},
1092         slaccitation = {\%\%CITATION = HEP-TH/0001129\\;\%\%},
1093         title = {{Algebraic quantum field theory, perturbation theory, and the loop expansion}},
1094         url = {http://arxiv.org/abs/hep-th/0001129},
1095         volume = {219},
1096         year = {2001}
1097 }
1098 
1099 @article{FassarellaSchroer:2001,
1100         abstract = {The well-known fact that classical automorphisms of (compactified) Minkowski spacetime (Poincare or conformal trandsformations) also allow a natural derivation/interpretation in the modular setting (in the operator-algebraic sense of Tomita and Takesaki) of the algebraic formulation of QFT has an interesting nontrivial chiral generalization to the diffeomorphisms of the circle. Combined with recent ideas on algebraic (d-1)-dimensional lightfront holography, these diffeomorphisms turn out to be images of ``fuzzy'' acting groups in the original d-dimensional (massive) QFT. These actions do not require any spacetime noncommutativity and are in complete harmony with causality and localization principles. Their use tightens the relation with kinematic chiral structures on the causal horizon and makes recent attempts to explain the required universal structure of a possible future quantum Bekenstein law in terms of Virasoro algebra structures more palatable.},
1101         author = {L. Fassarella and B. Schroer},
1102         eprint = {hep-th/0106064},
1103         localfile = {2001 - Fassarella, Schroer - The fuzzy analog of chiral diffeomorphisms in higher dimensional quantum field theories.pdf},
1104         slaccitation = {\%\%CITATION = HEP-TH/0106064\\;\%\%},
1105         title = {{The fuzzy analog of chiral diffeomorphisms in higher dimensional quantum field theories}},
1106         url = {http://arxiv.org/abs/hep-th/0106064},
1107         year = {2001}
1108 }
1109 
1110 @article{FewsterVerch:2002,
1111         abstract = {Quantum fields are well known to violate the weak energy condition of general relativity: the renormalised energy density at any given point is unbounded from below as a function of the quantum state. By contrast, for the scalar and electromagnetic fields it has been shown that weighted averages of the energy density along timelike curves satisfy `quantum weak energy inequalities' (QWEIs) which constitute lower bounds on these quantities. Previously, Dirac QWEIs have been obtained only for massless fields in two-dimensional spacetimes. In this paper we establish QWEIs for the Dirac and Majorana fields of mass $m\ge 0$ on general four-dimensional globally hyperbolic spacetimes, averaging along arbitrary smooth timelike curves with respect to any of a large class of smooth compactly supported positive weights. Our proof makes essential use of the microlocal characterisation of the class of Hadamard states, for which the energy density may be defined by point-splitting.},
1112         author = {C. J. Fewster and R. Verch},
1113         doi = {10.1007/s002200100584},
1114         eprint = {math-ph/0105027},
1115         journal = {Commun. Math. Phys.},
1116         localfile = {2001 - Fewster, Verch - A Quantum weak energy inequality for Dirac fields in curved space-time.pdf},
1117         pages = {331--359},
1118         slaccitation = {\%\%CITATION = MATH-PH/0105027\\;\%\%},
1119         title = {{A quantum weak energy inequality for Dirac fields in curved spacetime}},
1120         url = {http://arxiv.org/abs/math-ph/0105027},
1121         volume = {225},
1122         year = {2002}
1123 }
1124 
1125 @article{FleischhackLewandowski:2001,
1126         abstract = {It is shown that the definition of physical integration measures via ``exponential of minus the action times kinematical integration measure'' typically contradicts properties of physical models. In particular, theories with uncountably many non-vanishing Wilson-loop expectation values cannot be gained this way. The results are rigorous within the Ashtekar approach to gauge field theories.},
1127         author = {C. Fleischhack and J. Lewandowski},
1128         eprint = {math-ph/0111001},
1129         localfile = {2001 - Fleischhack, Lewandowski - Breakdown of the action method in gauge theories.pdf},
1130         slaccitation = {\%\%CITATION = MATH-PH/0111001\\;\%\%},
1131         title = {{Breakdown of the action method in gauge theories}},
1132         url = {http://arxiv.org/abs/math-ph/0111001},
1133         year = {2001}
1134 }
1135 
1136 @article{Fleischhack:2003-1,
1137         abstract = {The bundle structure of the space $\Ab$ of Ashtekar's generalized connections is investigated in the compact case. It is proven that every stratum is a locally trivial fibre bundle. The only stratum being a principal fibre bundle is the generic stratum. Its structure group equals the space $\Gb$ of all generalized gauge transforms modulo the constant center-valued gauge transforms. For abelian gauge theories the generic stratum is globally trivial and equals the total space $\Ab$. However, for a certain class of non-abelian gauge theories -- e.g., all SU(N) theories -- the generic stratum is nontrivial. This means, there are no global gauge fixings -- the so-called Gribov problem. Nevertheless, there is a covering of the generic stratum by trivializations each having total induced Haar measure 1.},
1138         author = {C. Fleischhack},
1139         eprint = {math-ph/0007001},
1140         journal = {Commun. Math. Phys.},
1141         localfile = {2003 - Fleischhack - On the Gribov problem for generalized connections.pdf},
1142         pages = {423--454},
1143         slaccitation = {\%\%CITATION = MATH-PH/0007001\\;\%\%},
1144         title = {{On the Gribov problem for generalized connections}},
1145         url = {http://arxiv.org/abs/math-ph/0007001},
1146         volume = {234},
1147         year = {2003}
1148 }
1149 
1150 @article{Fleischhack:2001,
1151         abstract = {It is indicated that the definition of physical measures via ``exponential of minus the action times kinematical measure'' contradicts properties of certain physical models. In particular, theories describing confinement typically cannot be gained this way. The results are rigorous within the Ashtekar approach to gauge field theories.},
1152         author = {C. Fleischhack},
1153         eprint = {math-ph/0107022},
1154         localfile = {2001 - Fleischhack - On the structure of physical measures in gauge theories.pdf},
1155         slaccitation = {\%\%CITATION = MATH-PH/0107022\\;\%\%},
1156         title = {{On the structure of physical measures in gauge theories}},
1157         url = {http://arxiv.org/abs/math-ph/0107022},
1158         year = {2001}
1159 }
1160 
1161 @article{Fleischhack:2001-1,
1162         abstract = {It is proven that the physical measure for the two-dimensional Yang-Mills theory is purely singular with respect to the kinematical Ashtekar-Lewandowski measure. For this, an explicit decomposition of the gauge orbit space into supports of these two measures is given. Finally, the results are extended to more general (e.g. confining) theories. Such a singularity implies, in particular, that the standard method of determining the physical measure via ``exponential of minus the action times kinematical measure'' is not applicable.},
1163         author = {C. Fleischhack},
1164         eprint = {math-ph/0109030},
1165         localfile = {2001 - Fleischhack - On the support of physical measures in gauge theories.pdf},
1166         slaccitation = {\%\%CITATION = MATH-PH/0109030\\;\%\%},
1167         title = {{On the support of physical measures in gauge theories}},
1168         url = {http://arxiv.org/abs/math-ph/0109030},
1169         year = {2001}
1170 }
1171 
1172 @article{Kunhardt:2001,
1173         abstract = {In quantum field theories with massless particles, states carrying a nontrivial superselection charge may have very poor localisation properties when compared to the vacuum. In this case, replacing the vacuum with a suitable ``infravacuum'' state can improve the localisability of the charges in such a way that the Doplicher-Haag-Roberts (DHR) theory of superselection sectors is applicable. As an explicit example for this phenomenon, we consider a certain class of sectors of the free massless scalar field. These sectors carry a charge of electric type, and the corresponding infravacuum background may be interpreted as a cloud of infrared radiation. Motivated by this situation, we propose a model-independent definition of infravacuum representations and derive some of their properties. We analyse in particular their role as reference representations for DHR theory and investigate to what an extent the absence of a translation invariant vector affects the results of the DHR analysis. Special emphasis is put on the functorial aspects of the theory and on the description of the covariance and the spectral properties of charged sectors in terms of so-called charge transporting cocycles.},
1174         author = {W. Kunhardt},
1175         eprint = {math-ph/0109001},
1176         localfile = {2001 - Kunhardt - On Infravacua and the Superselection Structure of Theories with Massless Particles.pdf},
1177         slaccitation = {\%\%CITATION = MATH-PH/0109001\\;\%\%},
1178         title = {{On infravacua and the superselection structure of theories with massless particles}},
1179         url = {http://arxiv.org/abs/math-ph/0109001},
1180         year = {2001}
1181 }
1182 
1183 @article{Mund:2001,
1184         abstract = {The geometric action of modular groups for wedge regions (Bisognano-Wichmann property) is derived from the principles of local quantum physics for a large class of Poincare covariant models in d=4. As a consequence, the CPT theorem holds for this class. The models must have a complete interpretation in terms of massive particles. The corresponding charges need not be localizable in compact regions: The most general case is admitted, namely localization in spacelike cones.},
1185         author = {J. Mund},
1186         eprint = {hep-th/0101227},
1187         journal = {Annales Henri Poincare},
1188         localfile = {2001 - Mund - The Bisognano Wichmann theorem for massive theories.pdf},
1189         pages = {907--926},
1190         slaccitation = {\%\%CITATION = HEP-TH/0101227\\;\%\%},
1191         title = {{The Bisognano-Wichmann theorem for massive theories}},
1192         url = {http://arxiv.org/abs/hep-th/0101227},
1193         volume = {2},
1194         year = {2001}
1195 }
1196 
1197 @article{Schroer:2001-1,
1198         abstract = {The limitations of the approach based on using fields restricted to the lightfront (Lightfront Quantization or p$\to \infty $ Frame Approach) which drive quantum fields towards canonical and ultimately free fields are well known. Here we propose a new concept which does not suffer from this limitation. It is based on a procedure which cannot be directly formulated in terms of pointlike fields but requires ``holographic'' manipulations of the algebras generated by those fields. We illustrate the new concepts in the setting of factorizable d=1+1 models and show that the known fact of absence of ultraviolet problems in those models (in the presence of higher than canonical dimensions) also passes to their holographic images. In higher spacetime dimensions d>=1+1 the holographic image lacks the transversal localizability; however this can be remedied by doing holography on d-2 additional lightfronts which share one lightray (Scanning by d-1 chiral conformal theories).},
1199         author = {B. Schroer},
1200         eprint = {hep-th/0108203},
1201         journal = {Preprint},
1202         localfile = {2001 - Schroer - Lightfront Formalism versus Holography + Chiral Scanning.pdf},
1203         slaccitation = {\%\%CITATION = HEP-TH/0108203\\;\%\%},
1204         title = {{Lightfront formalism versus holography and chiral scanning}},
1205         url = {http://arxiv.org/abs/hep-th/0108203},
1206         year = {2001}
1207 }
1208 
1209 @article{Schroer:2003,
1210         abstract = {It is shown that the operator algebraic setting of local quantum physics leads to a uniqueness proof for the inverse scattering problem. The important mathematical tool is the thermal KMS aspect of wedge-localized operator algebras and its strengthening by the requirement of crossing symmetry for generalized formfactors. The theorem extends properties which were previously seen in d=1+1 factorizing models.},
1211         author = {B. Schroer},
1212         eprint = {hep-th/0106066},
1213         journal = {Ann. Phys.},
1214         localfile = {2001 - Schroer - Uniqueness of Inverse Scattering Problem in Local Quantum Physics.pdf},
1215         pages = {421--437},
1216         slaccitation = {\%\%CITATION = HEP-TH/0106066\\;\%\%},
1217         title = {{Uniqueness of inverse scattering problem in local quantum physics}},
1218         url = {http://arxiv.org/abs/hep-th/0106066},
1219         volume = {307},
1220         year = {2003}
1221 }
1222 
1223 @article{Strohmaier:2000,
1224         abstract = {This paper investigates wave-equations on spacetimes with a metric which is locally analytic in the time. We use recent results in the theory of the non-characteristic Cauchy problem to show that a solution to a wave-equation vanishing in an open set vanishes in the ``envelope'' of this set, which may be considerably larger and in the case of timelike tubes may even coincide with the spacetime itself. We apply this result to the real scalar field on a globally hyperbolic spacetime and show that the field algebra of an open set and its envelope coincide. As an example there holds an analog of Borchers' timelike tube theorem for such scalar fields and hence, algebras associated with world lines can be explicitly given. Our result applies to cosmologically relevant spacetimes.},
1225         author = {A. Strohmaier},
1226         eprint = {math-ph/0008043},
1227         journal = {Lett. Math. Phys.},
1228         localfile = {2000 - Strohmaier - On the local structure of the Klein-Gordon field on curved spacetimes.pdf},
1229         pages = {249--261},
1230         slaccitation = {\%\%CITATION = MATH-PH/0008043\\;\%\%},
1231         title = {{On the local structure of the Klein-Gordon field on curved spacetimes}},
1232         url = {http://arxiv.org/abs/math-ph/0008043},
1233         volume = {54},
1234         year = {2000}
1235 }
1236 
1237 @article{Thiemann:2001,
1238         abstract = {This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called loop quantum gravity\". The term modern\" in the title refers to the fact that the quantum theory is based on formulating classical general relativity as a theory of connections rather than metrics as compared to in original version due to Arnowitt, Deser and Misner. Canonical quantum general relativity is an attempt to define a mathematically rigorous, non-perturbative, background independent theory of Lorentzian quantum gravity in four spacetime dimensions in the continuum. The approach is minimal in that one simply analyzes the logical consequences of combining the principles of general relativity with the principles of quantum mechanics. The requirement to preserve background independence has lead to new, fascinating mathematical structures which one does not see in perturbative approaches, e.g. a fundamental discreteness of spacetime seems to be a prediction of the theory providing a first substantial evidence for a theory in which the gravitational field acts as a natural UV cut-off. An effort has been made to provide a self-contained exposition of a restricted amount of material at the appropriate level of rigour which at the same time is accessible to graduate students with only basic knowledge of general relativity and quantum field theory on Minkowski space.},
1239         author = {T. Thiemann},
1240         eprint = {gr-qc/0110034},
1241         localfile = {2001 - Thiemann - Introduction to modern canonical quantum general relativity.pdf},
1242         slaccitation = {\%\%CITATION = GR-QC/0110034\\;\%\%},
1243         title = {{Introduction to modern canonical quantum general relativity}},
1244         url = {http://arxiv.org/abs/gr-qc/0110034},
1245         year = {2001}
1246 }
1247 
1248 @article{AshtekarLewandowskiSahlmann:2003,
1249         abstract = {In loop quantum gravity, matter fields can have support only on the `polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states can not refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background independent operator algebras and Hilbert spaces. Second, to make contact with low energy physics, one has to relate this `polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.},
1250         author = {A. Ashtekar and J. Lewandowski and H. Sahlmann},
1251         eprint = {gr-qc/0211012},
1252         journal = {Class. Quant. Grav.},
1253         localfile = {2002 - Ashtekar, Lewandowski, Sahlmann - Polymer and Fock representations for a Scalar field.pdf},
1254         pages = {L11--1},
1255         slaccitation = {\%\%CITATION = GR-QC/0211012\\;\%\%},
1256         title = {{Polymer and {F}ock representations for a scalar field}},
1257         url = {http://arxiv.org/abs/gr-qc/0211012},
1258         volume = {20},
1259         year = {2003}
1260 }
1261 
1262 @article{BahnsDoplicherFredenhagenPiacitelli:2002,
1263         abstract = {It is shown that the violation of unitarity observed in space/time noncommutative field theories is due to an improper definition of quantum field theory on noncommutative spacetime.},
1264         author = {D. Bahns and S. Doplicher and K. Fredenhagen and G. Piacitelli},
1265         doi = {10.1016/S0370-2693(02)01563-0},
1266         eprint = {hep-th/0201222},
1267         journal = {Phys. Lett.},
1268         keywords = {NCQFT},
1269         localfile = {2002 - Bahns, Doplicher, Fredenhagen, Piacitelli - On the unitarity problem in space-time noncommutative theories.pdf},
1270         pages = {178--181},
1271         slaccitation = {\%\%CITATION = HEP-TH/0201222\\;\%\%},
1272         title = {{On the unitarity problem in space/time noncommutative theories}},
1273         url = {http://arxiv.org/abs/hep-th/0201222},
1274         volume = {B533},
1275         year = {2002}
1276 }
1277 
1278 @article{BuchholzMundSummers:2002,
1279         abstract = {We propose a canonical description of the dynamics of quantum systems on a class of Robertson-Walker space-times. We show that the worldline of an observer in such space-times determines a unique orbit in the local conformal group SO(4,1) of the space-time and that this orbit determines a unique transport on the space-time. For a quantum system on the space-time modeled by a net of local algebras, the associated dynamics is expressed via a suitable family of ``propagators''. In the best of situations, this dynamics is covariant, but more typically the dynamics will be ``quasi-covariant'' in a sense we make precise. We then show by using our technique of ``transplanting'' states and nets of local algebras from de Sitter space to Robertson-Walker space that there exist quantum systems on Robertson-Walker spaces with quasi-covariant dynamics. The transplanted state is locally passive, in an appropriate sense, with respect to this dynamics.},
1280         author = {D. Buchholz and J. Mund and S. J. Summers},
1281         eprint = {hep-th/0207057},
1282         journal = {Class. Quant. Grav.},
1283         localfile = {2002 - Buchholz, Mund, Summers - Covariant and quasi-covariant quantum dynamics in Robertson-Walker space-times.pdf},
1284         pages = {6417--6434},
1285         slaccitation = {\%\%CITATION = HEP-TH/0207057\\;\%\%},
1286         title = {{Covariant and quasi-covariant quantum dynamics in Robertson-Walker space-times}},
1287         url = {http://arxiv.org/abs/hep-th/0207057},
1288         volume = {19},
1289         year = {2002}
1290 }
1291 
1292 @article{CastroAlvaredoFring:2003,
1293         abstract = {We compute the DC conductance with two different methods, which both exploit the integrability of the theories under consideration. On one hand we determine the conductance through a defect by means of the thermodynamic Bethe ansatz and standard relativistic potential scattering theory based on a Landauer transport theory picture. On the other hand, we propose a Kubo formula for a defect system and evaluate the current-current two-point correlation function it involves with the help of a form factor expansion. For a variety of defects in a fermionic system we find excellent agreement between the two different theoretical descriptions.},
1294         author = {O. Castro-Alvaredo and A. Fring},
1295         eprint = {hep-th/0205076},
1296         journal = {Nucl. Phys.},
1297         localfile = {2003 - Castro-Alvaredo, Fring - From integrability to conductance, impurity systems.pdf},
1298         pages = {449--490},
1299         slaccitation = {\%\%CITATION = HEP-TH/0205076\\;\%\%},
1300         title = {{From integrability to conductance, impurity systems}},
1301         url = {http://arxiv.org/abs/hep-th/0205076},
1302         volume = {B649},
1303         year = {2003}
1304 }
1305 
1306 @article{FassarellaSchroer:2002,
1307         abstract = {Wigner's irreducible positive energy representations of the Poincare group are often used to give additional justifications for the Lagrangian quantization formalism of standard QFT. Here we study another more recent aspect. We explain in this paper modular concepts by which we are able to construct the local operator algebras for all standard positive energy representations directly i.e. without going through field coordinatizations. In this way the artificial emphasis on Lagrangian field coordinates is avoided from the very beginning. These new concepts allow to treat also those cases of ``exceptional'' Wigner representations associated with anyons and the famous Wigner ``spin tower''which have remained inaccessible to Lagrangian quantization. Together with the d=1+1 factorizing models (whose modular construction has been studied previously), they form an interesting family of theories with a rich vacuum-polarization structure (but no on shell real particle creation) to which the modular methods can be applied for their explicit construction. We explain and illustrate the algebraic strategy of this construction. We also comment on possibilities of formulating the Wigner theory in a setting of a noncommutative spacetime substrate. This is potentially interesting in connection with recent unitarity- and Lorentz invariance- preserving results of the special nonlocality caused by this kind of noncommutativity.},
1308         author = {L. Fassarella and B. Schroer},
1309         eprint = {hep-th/0112168},
1310         journal = {J. Phys.},
1311         localfile = {2002 - Fassarella, Schroer - Wigner Particle Theory and Local Quantum Physics.pdf},
1312         pages = {9123--9164},
1313         slaccitation = {\%\%CITATION = HEP-TH/0112168\\;\%\%},
1314         title = {{Wigner particle theory and local quantum physics}},
1315         url = {http://arxiv.org/abs/hep-th/0112168},
1316         volume = {A35},
1317         year = {2002}
1318 }
1319 
1320 @article{Fleischhack:2003,
1321         author = {C. Fleischhack},
1322         journal = {J. Geom. Phys.},
1323         localfile = {2003 - Fleischhack - Regular connections among generalized connections.pdf},
1324         pages = {469--483},
1325         slaccitation = {\%\%CITATION = JGPHE,47,469\\;\%\%},
1326         title = {{Regular connections among generalized connections}},
1327         volume = {47},
1328         year = {2003}
1329 }
1330 
1331 @article{Sahlmann:2002,
1332         abstract = {Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is singled out by its elegance and diffeomorphism covariance. Recently, in the context of the quest for semiclassical states, states of the theory in which the quantum gravitational field is close to some classical geometry, it was realized that it might also be worthwhile to study different representations of the algebra A of observables. The content of the present note is the observation that under some mild assumptions, the mathematical structure of representations of A can be analyzed rather effortlessly, to a certain extent: Each representation can be labeled by sets of functions and measures on the space of (generalized) connections that fulfill certain conditions. These considerations are however mostly of mathematical nature. Their physical content remains to be clarified, and physically interesting examples are yet to be constructed.},
1333         author = {H. Sahlmann},
1334         eprint = {gr-qc/0207111},
1335         localfile = {2002 - Sahlmann - Some comments on the representation theory of the algebra underlying loop quantum gravity.pdf},
1336         slaccitation = {\%\%CITATION = GR-QC/0207111\\;\%\%},
1337         title = {{Some comments on the representation theory of the algebra underlying loop quantum gravity}},
1338         url = {http://arxiv.org/abs/gr-qc/0207111},
1339         year = {2002}
1340 }
1341 
1342 @article{Thiemann:2003,
1343         abstract = {Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured over the past fifteen years to a mathematically rigorous candidate quantum field theory of the gravitational field. The features that distinguish it from other quantum gravity theories are 1) background independence and 2) minimality of structures. Background independence means that this is a non-perturbative approach in which one does not perturb around a given, distinguished, classical background metric, rather arbitrary fluctuations are allowed, thus precisely encoding the quantum version of Einstein's radical perception that gravity is geometry. Minimality here means that one explores the logical consequences of bringing together the two fundamental principles of modern physics, namely general covariance and quantum theory, without adding any experimentally unverified additional structures. The approach is purposely conservative in order to systematically derive which basic principles of physics have to be given up and must be replaced by more fundamental ones. QGR unifies all presently known interactions in a new sense by quantum mechanically implementing their common symmetry group, the four-dimensional diffeomorphism group, which is almost completely broken in perturbative approaches. These lectures offer a problem -- supported introduction to the subject.},
1344         author = {T. Thiemann},
1345         eprint = {gr-qc/0210094},
1346         journal = {Lect. Notes Phys.},
1347         localfile = {2003 - Thiemann - Lectures on loop quantum gravity.pdf},
1348         pages = {41--135},
1349         slaccitation = {\%\%CITATION = GR-QC/0210094\\;\%\%},
1350         title = {{Lectures on loop quantum gravity}},
1351         url = {http://arxiv.org/abs/gr-qc/0210094},
1352         volume = {631},
1353         year = {2003}
1354 }
1355 
1356 @article{AlvarezGaumeVazquezMozo:2003,
1357         abstract = {In this paper we study general properties of noncommutative field theories obtained from the Seiberg-Witten limit of string theories in the presence of an external B-field. We analyze the extension of the Wightman axioms to this context and explore their consequences, in particular we present a proof of the CPT theorem for theories with space-space noncommutativity. We analyze as well questions associated to the spin-statistics connections, and show that noncommutative N=4, U(1) gauge theory can be softly broken to N=0 satisfying the axioms and providing an example where the Wilsonian low energy effective action can be constructed without UV/IR problems, after a judicious choice of soft breaking parameters is made. We also assess the phenomenological prospects of such a theory, which are in fact rather negative.},
1358         author = {L. Alvarez-Gaume and M. A. Vazquez-Mozo},
1359         druck = {Booklet 22.07.08},
1360         eprint = {hep-th/0305093},
1361         journal = {Nucl. Phys.},
1362         keywords = {NCQFT},
1363         localfile = {2003 - Alvarez-Gaume, Vazquez-Mozo - General Properties of Noncommutative Field Theories.pdf},
1364         pages = {293--321},
1365         slaccitation = {\%\%CITATION = HEP-TH/0305093\\;\%\%},
1366         title = {{General properties of noncommutative field theories}},
1367         url = {http://arxiv.org/abs/hep-th/0305093},
1368         volume = {B668},
1369         year = {2003}
1370 }
1371 
1372 @article{BabujianKarowski:2004,
1373         abstract = {The purpose of the ``bootstrap program'' for integrable quantum field theories in 1+1 dimensions is to construct a model in terms of its Wightman functions explicitly. In this article, this program is mainly illustrated in terms of the sine-Gordon and the sinh-Gordon model and (as an exercise) the scaling Ising model. We review some previous results on sine-Gordon breather form factors and quantum operator equations. The problem to sum over intermediate states is attacked in the short distance limit of the two point Wightman function for the sinh-Gordon and the scaling Ising model.},
1374         author = {H. M. Babujian and M. Karowski},
1375         eprint = {hep-th/0301088},
1376         journal = {Int. J. Mod. Phys.},
1377         localfile = {2003 - Babujian, Karowski - Towards the Construction of Wightman Functions of Integrable Quantum Field Theories.pdf},
1378         pages = {34--49},
1379         slaccitation = {\%\%CITATION = HEP-TH/0301088\\;\%\%},
1380         title = {{Towards the construction of Wightman functions of integrable quantum field theories}},
1381         url = {http://arxiv.org/abs/hep-th/0301088},
1382         volume = {A19S2},
1383         year = {2004}
1384 }
1385 
1386 @article{ChaichianNishijimaTureanu:2003,
1387         abstract = {We show that Pauli's spin-statistics relation remains valid in noncommutative quantum field theories (NC QFT), with the exception of some peculiar cases of noncommutativity between space and time. We also prove that, while the individual symmetries C and T, and in some cases also P, are broken, the CPT theorem still holds in general for noncommutative field theories, in spite of the inherent nonlocality and violation of Lorentz invariance.},
1388         author = {M. Chaichian and K. Nishijima and A. Tureanu},
1389         druck = {Booklet 24.07.08},
1390         eprint = {hep-th/0209008},
1391         journal = {Phys. Lett.},
1392         keywords = {NCQFT},
1393         localfile = {2003 - Chaichian, Nishijima, Tureanu - Spin-Statistics and CPT Theorems in Noncommutative Field Theory.pdf},
1394         pages = {146--152},
1395         slaccitation = {\%\%CITATION = HEP-TH/0209008\\;\%\%},
1396         title = {{Spin-statistics and CPT theorems in noncommutative field theory}},
1397         url = {http://arxiv.org/abs/hep-th/0209008},
1398         volume = {B568},
1399         year = {2003}
1400 }
1401 
1402 @article{Fleischhack:2003-2,
1403         abstract = {For connected reductive linear algebraic structure groups it is proven that every web is holonomically isolated. The possible tuples of parallel transports in a web form a Lie subgroup of the corresponding power of the structure group. This Lie subgroup is explicitly calculated and turns out to be independent of the chosen local trivializations. Moreover, explicit necessary and sufficient criteria for the holonomical independence of webs are derived. The results above can even be sharpened: Given an arbitrary neighbourhood of the base points of a web, then this neighbourhood contains some segments of the web whose parameter intervals coincide, but do not include 0 (that corresponds to the base points of the web), and whose parallel transports already form the same Lie subgroup as those of the full web do.},
1404         author = {C. Fleischhack},
1405         eprint = {math-ph/0304001},
1406         localfile = {2003 - Fleischhack - Parallel Transports in Webs.pdf},
1407         slaccitation = {\%\%CITATION = MATH-PH/0304001\\;\%\%},
1408         title = {{Parallel Transports in Webs}},
1409         url = {http://arxiv.org/abs/math-ph/0304001},
1410         year = {2003}
1411 }
1412 
1413 @article{Fleischhack:2004,
1414         abstract = {It is proven that for compact, connected and semisimple structure groups every degenerate labelled web is strongly degenerate. This conjecture by Lewandowski and Thiemann implies that diffeomorphism invariant operators in the category of piecewise smooth immersive paths preserve the decomposition of the space of integrable functions w.r.t. the degeneracy and symmetry of the underlying labelled webs. This property is necessary for lifting these operators to well-defined operators on the space of diffeomorphism invariant states.},
1415         author = {C. Fleischhack},
1416         eprint = {math-ph/0304002},
1417         journal = {Commun. Math. Phys.},
1418         localfile = {2004 - Fleischhack - Proof of a Conjecture by Lewandowski and Thiemann.pdf},
1419         pages = {331--352},
1420         slaccitation = {\%\%CITATION = MATH-PH/0304002\\;\%\%},
1421         title = {{Proof of a Conjecture by Lewandowski and Thiemann}},
1422         url = {http://arxiv.org/abs/math-ph/0304002},
1423         volume = {249},
1424         year = {2004}
1425 }
1426 
1427 @article{Jkel:2004,
1428         abstract = {Given a thermal field theory for some temperature $\beta^{-1}$, we construct the theory at an arbitrary temperature $ 1 / \beta'$. Our work is based on a construction invented by Buchholz and Junglas, which we adapt to thermal field theories. In a first step we construct states which closely resemble KMS states for the new temperature in a local region $\O_\circ \subset \rr^4$, but coincide with the given KMS state in the space-like complement of a slightly larger region $\hat{\O}$. By a weak*-compactness argument there always exists a convergent subnet of states as the size of $ \O_\circ$ and $ \hat{\O}$ tends towards $ \rr^4$. Whether or not such a limit state is a global KMS state for the new temperature, depends on the surface energy contained in the layer in between the boundaries of $ \O_\circ$ and $ \hat{\O}$. We show that this surface energy can be controlled by a generalized cluster condition.},
1429         author = {C. D. J{\"{a}}kel},
1430         eprint = {hep-th/9803245},
1431         journal = {Annales Henri Poincare},
1432         localfile = {2004 - J\"{a}kel -%20 The Relation between KMS states for different temperatures.pdf},
1433         pages = {579--606},
1434         slaccitation = {\%\%CITATION = HEP-TH/9803245\\;\%\%},
1435         title = {{The relation between KMS-states for different temperatures}},
1436         url = {http://arxiv.org/abs/hep-th/9803245},
1437         volume = {5},
1438         year = {2004}
1439 }
1440 
1441 @article{RedeiSummers:2003,
1442         abstract = {It is shown that the correlations predicted by relativistic quantum field theory in locally normal states between projections in local von Neumann algebras $\cA(V_1),\cA(V_2)$ associated with spacelike separated spacetime regions $V_1,V_2$ have a (Reichenbachian) common cause located in the union of the backward light cones of $V_1$ and $V_2$. Further comments on causality and independence in quantum field theory are made.},
1443         author = {M. Redei and S. J. Summers},
1444         eprint = {quant-ph/0302115},
1445         localfile = {2003 - Redei, Summers - Remarks On Causality in Relativistic Quantum Field Theory.pdf},
1446         slaccitation = {\%\%CITATION = QUANT-PH/0302115\\;\%\%},
1447         title = {{Remarks on Causality in Relativistic Quantum Field Theory}},
1448         url = {http://arxiv.org/abs/quant-ph/0302115},
1449         year = {2003}
1450 }
1451 
1452 @article{Wess:2003,
1453         abstract = {Lecture given at BW2003 Workshop Mathematical, Theoretical and Phenomenological Challenges Beyond Standard Model\" 29 August-02 September, 2003 Vrnjacka Banja, Serbia},
1454         author = {J. Wess},
1455         eprint = {hep-th/0408080},
1456         localfile = {2003 - Wess - Deformed coordinate spaces: Derivatives.pdf},
1457         slaccitation = {\%\%CITATION = HEP-TH/0408080\\;\%\%},
1458         title = {{Deformed coordinate spaces: Derivatives}},
1459         url = {http://arxiv.org/abs/hep-th/0408080},
1460         year = {2003}
1461 }
1462 
1463 @article{Bostelmann:2005,
1464         abstract = {The paper investigates relations between the phase space structure of a quantum field theory (nuclearity\") and the concept of pointlike localized fields. Given a net of local observable algebras, a phase space condition is introduced that allows a very detailed description of the theory's field content. An appendix discusses noninteracting models as examples.},
1465         author = {H. Bostelmann},
1466         eprint = {math-ph/0409070},
1467         journal = {J. Math. Phys.},
1468         localfile = {2004 - Bostelmann - Phase space properties and the short distance structure in quantum field theory.pdf},
1469         pages = {052301},
1470         slaccitation = {\%\%CITATION = MATH-PH/0409070\\;\%\%},
1471         title = {{Phase space properties and the short distance structure in quantum field theory}},
1472         url = {http://arxiv.org/abs/math-ph/0409070},
1473         volume = {46},
1474         year = {2005}
1475 }
1476 
1477 @article{BuchholzLechner:2004,
1478         abstract = {Within the algebraic setting of quantum field theory, a condition is given which implies that the intersection of algebras generated by field operators localized in wedge--shaped regions of two--dimensional Minkowski space is non--trivial; in particular, there exist compactly localized operators in such theories which can be interpreted as local observables. The condition is based on spectral (nuclearity) properties of the modular operators affiliated with wedge algebras and the vacuum state and is of interest in the algebraic approach to the formfactor program, initiated by Schroer. It is illustrated here in a simple class of examples.},
1479         author = {D. Buchholz and G. Lechner},
1480         doi = {10.1007/s00023-004-0190-8},
1481         eprint = {math-ph/0402072},
1482         journal = {Annales Henri Poincar\'{e}},
1483         localfile = {2004 - Buchholz, Lechner - Modular nuclearity and localization.pdf},
1484         pages = {1065--1080},
1485         slaccitation = {\%\%CITATION = MATH-PH/0402072\\;\%\%},
1486         title = {{Modular nuclearity and localization}},
1487         url = {http://arxiv.org/abs/math-ph/0402072},
1488         volume = {5},
1489         x-color = {#199bff},
1490         year = {2004}
1491 }
1492 
1493 @article{ChaichianMnatsakanovaNishijimaTureanuVernov:2004,
1494         abstract = {We propose new Wightman functions as vacuum expectation values of products of field operators in the \nc space-time. These Wightman functions involve the $\star$-product. In the case of only space-space \ncy ($\theta_{0i}=0$), we prove the CPT theorem using the \nc form of the Wightman functions. As a byproduct, one arrives at the general conclusion of the following theorem that the violation of CPT invariance implies the violation of not only Lorentz invariance, but also its subgroup of symmetry $SO(1,1)\times SO(2)$. We also show that the spin-statistics theorem, for the simplest case of a scalar field, holds within this formalism.},
1495         author = {M. Chaichian and M. N. Mnatsakanova and K. Nishijima and A. Tureanu and Y. S. Vernov},
1496         comments = {Only space-space NC, space and time commute},
1497         eprint = {hep-th/0402212},
1498         journal = {Preprint},
1499         keywords = {NCQFT},
1500         localfile = {2004 - Chaichian, Mnatsakanova, Nishijima, Tureanu, Vernov - Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory.pdf},
1501         slaccitation = {\%\%CITATION = HEP-TH/0402212\\;\%\%},
1502         title = {{Towards an axiomatic formulation of noncommutative quantum field theory}},
1503         url = {http://arxiv.org/abs/hep-th/0402212},
1504         volume = {arXiv: hep-th/0402212},
1505         year = {2004}
1506 }
1507 
1508 @article{Fewster:2004,
1509         abstract = {In a recent preprint, Krasnikov has claimed that to show that quantum energy inequalities (QEIs) are violated in curved spacetime situations, by considering the example of a free massless scalar field in two-dimensional de Sitter space. We show that this claim is incorrect, and based on misunderstandings of the nature of QEIs. We also prove, in general two-dimensional spacetimes, that flat spacetime QEIs give a good approximation to the curved spacetime results on sampling timescales short in comparison with natural geometric scales.},
1510         author = {C. J. Fewster},
1511         eprint = {gr-qc/0409043},
1512         localfile = {2004 - Fewster - Comments on 'Counter example to the quantum inequality'.pdf},
1513         slaccitation = {\%\%CITATION = GR-QC/0409043\\;\%\%},
1514         title = {{Comments on 'Counter example to the quantum inequality'}},
1515         url = {http://arxiv.org/abs/gr-qc/0409043},
1516         year = {2004}
1517 }
1518 
1519 @article{Fewster:2004-1,
1520         abstract = {Quantum energy inequalities (QEIs) were established by Flanagan for the massless scalar field on two-dimensional Lorentzian spacetimes globally conformal to Minkowski space. We extend his result to all two-dimensional globally hyperbolic Lorentzian spacetimes and use it to show that flat spacetime QEIs give a good approximation to the curved spacetime results on sampling timescales short in comparison with natural geometric scales. This is relevant to the application of QEIs to constrain exotic spacetime metrics.},
1521         author = {C. J. Fewster},
1522         eprint = {gr-qc/0411114},
1523         journal = {Phys. Rev.},
1524         localfile = {2004 - Fewster - Quantum energy inequalities in two dimensions.pdf},
1525         pages = {127501},
1526         slaccitation = {\%\%CITATION = GR-QC/0411114\\;\%\%},
1527         title = {{Quantum energy inequalities in two dimensions}},
1528         url = {http://arxiv.org/abs/gr-qc/0411114},
1529         volume = {D70},
1530         year = {2004}
1531 }
1532 
1533 @article{KawahigashiLongo:2005,
1534         abstract = {We consider an intrinsic entropy associated with a local conformal net A by the coefficients in the expansion of the logarithm of the trace of the ``heat kernel'' semigroup. In analogy with Weyl theorem on the asymptotic density distribution of the Laplacian eigenvalues, passing to a quantum system with infinitely many degrees of freedom, we regard these coefficients as noncommutative geometric invariants. Under a natural modularity assumption, the leading term of the entropy (noncommutative area) is proportional to the central charge c, the first order correction (noncommutative Euler characteristic) is proportional to log\mu\_A, where \mu\_A is the global index of A, and the second spectral invariant is again proportional to c. We give a further general method to define a mean entropy by considering conformal symmetries that preserve a discretization of S^1 and we get the same value proportional to c. We then make the corresponding analysis with the proper Hamiltonian associated to an interval. We find here, in complete generality, a proper mean entropy proportional to log\\mu\_A with a first order correction defined by means of the relative entropy associated with canonical states. By considering a class of black holes with an associated conformal quantum field theory on the horizon, and relying on arguments in the literature, we indicate a possible way to link the noncommutative area with the Bekenstein-Hawking classical area description of entropy.},
1535         author = {Y. Kawahigashi and R. Longo},
1536         eprint = {math-ph/0405037},
1537         journal = {Commun. Math. Phys.},
1538         localfile = {2004 - Kawahigashi, Longo - Noncommutative Spectral Invariants and Black Hole Entropy.pdf},
1539         pages = {193--225},
1540         slaccitation = {\%\%CITATION = MATH-PH/0405037\\;\%\%},
1541         title = {{Noncommutative Spectral Invariants and Black Hole Entropy}},
1542         url = {http://arxiv.org/abs/math-ph/0405037},
1543         volume = {257},
1544         year = {2005}
1545 }
1546 
1547 @article{Lechner:2005,
1548         abstract = {A recently proposed criterion for the existence of local quantum fields with a prescribed factorizing scattering matrix is verified in a non-trivial model, thereby establishing a new constructive approach to quantum field theory in a particular example. The existence proof is accomplished by analyzing nuclearity properties of certain specific subsets of Fermionic Fock spaces.},
1549         author = {G. Lechner},
1550         doi = {10.1088/0305-4470},
1551         eprint = {math-ph/0405062},
1552         journal = {J. Phys.},
1553         localfile = {2005 - Lechner - On the existence of local observables in theories with a factorizing S-Matrix.pdf},
1554         pages = {3045--3056},
1555         slaccitation = {\%\%CITATION = MATH-PH/0405062\\;\%\%},
1556         title = {{On the existence of local observables in theories with a factorizing S-matrix}},
1557         url = {http://arxiv.org/abs/math-ph/0405062},
1558         volume = {A38},
1559         x-color = {#199bff},
1560         year = {2005}
1561 }
1562 
1563 @article{LongoRehren:2004,
1564         abstract = {Conformal field theory on the half-space x\&gt;0 of Minkowski space-time (boundary CFT\") is analyzed from an algebraic point of view, clarifying in particular the algebraic structure of local algebras and the bi-localized charge structure of local fields. The field content and the admissible boundary conditions are characterized in terms of a non-local chiral field algebra.},
1565         author = {R. Longo and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
1566         doi = {10.1142/S0129055X04002163},
1567         eprint = {math-ph/0405067},
1568         journal = {Rev. Math. Phys.},
1569         localfile = {2004 - Longo, Rehren - Local fields in boundary conformal QFT.pdf},
1570         pages = {909},
1571         slaccitation = {\%\%CITATION = MATH-PH/0405067\\;\%\%},
1572         title = {{Local fields in boundary conformal {QFT}}},
1573         url = {http://arxiv.org/abs/math-ph/0405067},
1574         volume = {16},
1575         year = {2004}
1576 }
1577 
1578 @article{Schroer:2005,
1579         abstract = {Ever since the appearance of renormalization theory there have been several differently motivated attempts at non-localized (in the sense of not generated by point-like fields) relativistic particle theories, the most recent one being at QFT on non-commutative Minkowski spacetime. The often conceptually uncritical and historically forgetful contemporary approach to these problems calls for a critical review the light of previous results on this subject.},
1580         author = {B. Schroer},
1581         eprint = {hep-th/0405105},
1582         journal = {Ann. Phys.},
1583         localfile = {2005 - Schroer - An anthology of non-local QFT and QFT on noncommutative spacetime.pdf},
1584         pages = {92--122},
1585         slaccitation = {\%\%CITATION = HEP-TH/0405105\\;\%\%},
1586         title = {{An anthology of non-local QFT and QFT on noncommutative spacetime}},
1587         url = {http://arxiv.org/abs/hep-th/0405105},
1588         volume = {319},
1589         year = {2005}
1590 }
1591 
1592 @article{Ullrich:2004,
1593         author = {P. Ullrich},
1594         journal = {J. Math. Phys.},
1595         localfile = {2004 - Ullrich - On the restriction of quantum fields to a lightlike surface.pdf},
1596         pages = {3109--3145},
1597         slaccitation = {\%\%CITATION = JMAPA,45,3109\\;\%\%},
1598         title = {{On the restriction of quantum fields to a lightlike surface}},
1599         volume = {45},
1600         year = {2004}
1601 }
1602 
1603 @article{Yngvason:2005,
1604         abstract = {One of von Neumann's motivations for developing the theory of operator algebras and his and Murray's 1936 classification of factors was the question of possible decompositions of quantum systems into independent parts. For quantum systems with a finite number of degrees of freedom the simplest possibility, i.e., factors of type I in the terminology of Murray and von Neumann, are perfectly adequate. In relativistic quantum field theory (RQFT), on the other hand, factors of type III occur naturally. The same holds true in quantum statistical mechanics of infinite systems. In this brief review some physical consequences of the type III property of the von Neumann algebras corresponding to localized observables in RQFT and their difference from the type I case will be discussed. The cumulative effort of many people over more than 30 years has established a remarkable uniqueness result: The local algebras in RQFT are generically isomorphic to the unique, hyperfinite type ${III}_{1}$ factor in Connes' classification of 1973. Specific theories are characterized by the net structure of the collection of these isomorphic algebras for different space-time regions, i.e., the way they are embedded into each other.},
1605         author = {J. Yngvason},
1606         eprint = {math-ph/0411058},
1607         journal = {Rept. Math. Phys.},
1608         localfile = {2004 - Yngvason - The role of type III factors in quantum field theory.pdf},
1609         pages = {135--147},
1610         slaccitation = {\%\%CITATION = MATH-PH/0411058\\;\%\%},
1611         title = {{The role of type III factors in quantum field theory}},
1612         url = {http://arxiv.org/abs/math-ph/0411058},
1613         volume = {55},
1614         year = {2005}
1615 }
1616 
1617 @article{BahnsDoplicherFredenhagenPiacitelli:2005,
1618         abstract = {We give a definition of admissible counterterms appropriate for massive quantum field theories on the noncommutative Minkowski space, based on a suitable notion of locality. We then define products of fields of arbitrary order, the so-called quasiplanar Wick products, by subtracting only such admissible counterterms. We derive the analogue of Wick's theorem and comment on the consequences of using quasiplanar Wick products in the perturbative expansion.},
1619         author = {D. Bahns and S. Doplicher and K. Fredenhagen and G. Piacitelli},
1620         eprint = {hep-th/0408204},
1621         journal = {Phys. Rev.},
1622         keywords = {NCQFT},
1623         localfile = {2005 - Bahns, Doplicher, Fredenhagen, Piacitelli - Field Theory on Noncommutative Spacetimes - Quasiplanar Wick Products.pdf},
1624         pages = {025022},
1625         slaccitation = {\%\%CITATION = HEP-TH/0408204\\;\%\%},
1626         title = {{Field theory on noncommutative spacetimes: Quasiplanar Wick products}},
1627         url = {http://arxiv.org/abs/hep-th/0408204},
1628         volume = {D71},
1629         year = {2005}
1630 }
1631 
1632 @article{BalachandranManganoPinzulVaidya:2006,
1633         abstract = {The Groenewold-Moyal plane is the algebra A\_\theta(R^(d+1)) of functions on R^(d+1) with the star-product as the multiplication law, and the commutator [\x\_\mu\,x\_\nu] =i {\th}\eta\_{\mu \nu} between the coordinate functions. Chaichian et al. and Aschieri et al. have proved that the Poincare group acts as automorphisms on $A_\theta(R^(d+1))$ if the coproduct is deformed. (See also the prior work of Majid, Oeckl and Grosse et al). In fact, the diffeomorphism group with a deformed coproduct also does so according to the results of Aschieri et al. In this paper we show that for this new action, the Bose and Fermi commutation relations are deformed as well. Their potential applications to the quantum Hall effect are pointed out. Very striking consequences of these deformations are the occurrence of Pauli-forbidden energy levels and transitions. Such new effects are discussed in simple cases.},
1634         author = {A. P. Balachandran and G. Mangano and A. Pinzul and S. Vaidya},
1635         eprint = {hep-th/0508002},
1636         journal = {Int. J. Mod. Phys.},
1637         keywords = {NCQFT},
1638         localfile = {2005 - Balachandran, Mangano, Pinzul, Vaidya - Spin and Statistics on the Groenewold-Moyal Plane - Pauli-Forbidden Levels and Transitions.pdf},
1639         pages = {3111--3126},
1640         slaccitation = {\%\%CITATION = HEP-TH/0508002\\;\%\%},
1641         title = {{Spin and statistics on the Groenwald-Moyal plane: Pauli- forbidden levels and transitions}},
1642         url = {http://arxiv.org/abs/hep-th/0508002},
1643         volume = {A21},
1644         year = {2006}
1645 }
1646 
1647 @article{BuchholzSummers:2005,
1648         abstract = {We provide a brief overview of the basic tools and concepts of quantum field theoretical scattering theory. This article is commissioned by the Encyclopedia of Mathematical Physics, edited by J.-P. Francoise, G. Naber and T.S. Tsun, to be published by the Elsevier publishing house.},
1649         author = {D. Buchholz and S. J. Summers},
1650         eprint = {math-ph/0509047},
1651         journal = {Preprint},
1652         localfile = {2005 - Buchholz, Summers - Scattering in Relativistic Quantum Field Theory - Fundamental Concepts and Tools.pdf},
1653         slaccitation = {\%\%CITATION = MATH-PH/0509047\\;\%\%},
1654         title = {{Scattering in relativistic quantum field theory: Fundamental concepts and tools}},
1655         url = {http://arxiv.org/abs/math-ph/0509047},
1656         year = {2005}
1657 }
1658 
1659 @article{FewsterHollands:2005,
1660         abstract = {Quantum energy inequalities (QEIs) are state-independent lower bounds on weighted averages of the stress-energy tensor, and have been established for several free quantum field models. We present rigorous QEI bounds for a class of interacting quantum fields, namely the unitary, positive energy conformal field theories (with stress-energy tensor) on two-dimensional Minkowski space. The QEI bound depends on the weight used to average the stress-energy tensor and the central charge(s) of the theory, but not on the quantum state. We give bounds for various situations: averaging along timelike, null and spacelike curves, as well as over a spacetime volume. In addition, we consider boundary conformal field theories and more general 'moving mirror' models. Our results hold for all theories obeying a minimal set of axioms which -- as we show -- are satisfied by all models built from unitary highest-weight representations of the Virasoro algebra. In particular, this includes all (unitary, positive energy) minimal models and rational conformal field theories. Our discussion of this issue collects together (and, in places, corrects) various results from the literature which do not appear to have been assembled in this form elsewhere.},
1661         author = {C. J. Fewster and S. Hollands},
1662         eprint = {math-ph/0412028},
1663         journal = {Rev. Math. Phys.},
1664         localfile = {2005 - Fewster, Hollands - Quantum energy inequalities in two-dimensional conformal field theory.pdf},
1665         pages = {577},
1666         slaccitation = {\%\%CITATION = MATH-PH/0412028\\;\%\%},
1667         title = {{Quantum energy inequalities in two-dimensional conformal field theory}},
1668         url = {http://arxiv.org/abs/math-ph/0412028},
1669         volume = {17},
1670         year = {2005}
1671 }
1672 
1673 @article{GrosseWulkenhaar:2005,
1674         abstract = {We prove that the real four-dimensional Euclidean noncommutative \phi^4-model is renormalisable to all orders in perturbation theory. Compared with the commutative case, the bare action of relevant and marginal couplings contains necessarily an additional term: an harmonic oscillator potential for the free scalar field action. This entails a modified dispersion relation for the free theory, which becomes important at large distances (UV/IR-entanglement). The renormalisation proof relies on flow equations for the expansion coefficients of the effective action with respect to scalar fields written in the matrix base of the noncommutative R^4. The renormalisation flow depends on the topology of ribbon graphs and on the asymptotic and local behaviour of the propagator governed by orthogonal Meixner polynomials.},
1675         author = {H. Grosse and R. Wulkenhaar},
1676         eprint = {hep-th/0401128},
1677         journal = {Commun. Math. Phys.},
1678         localfile = {2005 - Grosse, Wulkenhaar - Renormalisation of phi**4 theory on noncommutative R**4 in the matrix base.pdf},
1679         pages = {305--374},
1680         slaccitation = {\%\%CITATION = HEP-TH/0401128\\;\%\%},
1681         title = {{Renormalisation of phi**4 theory on noncommutative R**4 in the matrix base}},
1682         url = {http://arxiv.org/abs/hep-th/0401128},
1683         volume = {256},
1684         year = {2005}
1685 }
1686 
1687 @article{Lechner:2007,
1688         abstract = {Starting from a given factorizing S-matrix $S$ in two space-time dimensions, we review a novel strategy to rigorously construct quantum field theories describing particles whose interaction is governed by $S$. The construction procedure is divided into two main steps: Firstly certain semi-local Wightman fields are introduced by means of Zamolodchikov's algebra. The second step consists in proving the existence of local observables in these models. As a new result, an intermediate step in the existence problem is taken by proving the modular compactness condition for wedge algebras.},
1689         author = {G. Lechner},
1690         journal = {Prog.Math.},
1691         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
1692         localfile = {2005 - Lechner - Towards the construction of quantum field theories from a factorizing S-matrix.pdf},
1693         pages = {175--198},
1694         pdf = {http://arxiv.org/pdf/hep-th/0502184},
1695         title = {{Towards the construction of quantum field theories from a factorizing S-matrix}},
1696         url = {http://arxiv.org/abs/hep-th/0502184},
1697         v1descr = {Mon, 21 Feb 2005 15:33:00 GMT (26kb)},
1698         volume = {251},
1699         x-color = {#199bff},
1700         year = {2007}
1701 }
1702 
1703 @article{MnatsakanovaVernov:2005,
1704         abstract = {The existence of Jost-Lehmann-Dyson representation analogue has been proved in framework of space-space noncommutative quantum field theory. On the basis of this representation it has been found that some class of elastic amplitudes admits an analytical continuation into complex \cos\vartheta plane and corresponding domain of analyticity is Martin ellipse. This analyticity combined with unitarity leads to Froissart-Martin upper bound on total cross section.},
1705         author = {M. N. Mnatsakanova and Y. S. Vernov},
1706         eprint = {hep-th/0403033},
1707         journal = {Theor. Math. Phys.},
1708         localfile = {2005 - Mnatsakanova, Vernov - Jost-Lehmann-Dyson representation, analyticity in angle variable and upper bounds in noncommutative quantum field theory.pdf},
1709         pages = {324--336},
1710         slaccitation = {\%\%CITATION = HEP-TH/0403033\\;\%\%},
1711         title = {{Jost-Lehmann-Dyson representation, analyticity in angle variable and upper bounds in noncommutative quantum field theory}},
1712         url = {http://arxiv.org/abs/hep-th/0403033},
1713         volume = {142},
1714         year = {2005}
1715 }
1716 
1717 @article{MundSchroerYngvason:2006,
1718         abstract = {We study free, covariant, quantum (Bose) fields that are associated with irreducible representations of the Poincar\'{e} group and localized in semi-infinite strings extending to spacelike infinity. Among these are fields that generate the irreducible representations of mass zero and infinite spin that are known to be incompatible with point-like localized fields. For the massive representation and the massless representations of finite helicity, all string-localized free fields can be written as an integral, along the string, of point-localized tensor or spinor fields. As a special case we discuss the string-localized vector fields associated with the point-like electromagnetic field and their relation to the axial gauge condition in the usual setting.},
1719         author = {J. Mund and B. Schroer and J. Yngvason},
1720         doi = {10.1007/s00220-006-0067-4},
1721         eprint = {math-ph/0511042},
1722         journal = {Commun. Math. Phys.},
1723         localfile = {2005 - Mund, Schroer, Yngvason - String-localized quantum fields and modular localization.pdf},
1724         pages = {621--672},
1725         slaccitation = {\%\%CITATION = MATH-PH/0511042\\;\%\%},
1726         title = {{String-localized quantum fields and modular localization}},
1727         url = {http://arxiv.org/abs/math-ph/0511042},
1728         volume = {268},
1729         year = {2006}
1730 }
1731 
1732 @article{Saffary:2005,
1733         abstract = {The subject of this thesis is the modular group of automorphisms acting on the massive algebra of local observables having their support in bounded open subsets of Minkowski space. After a compact introduction to micro-local analysis and the theory of one-parameter groups of automorphisms, which are used exensively throughout the investigation, we are concerned with modular theory and its consequences in mathematics, e.g., Connes' cocycle theorem and classification of type III factors and Jones' index theory, as well as in physics, e.g., the determination of local von Neumann algebras to be hyperfinite factors of type III\_1, the formulation of thermodynamic equilibrium states for infinite-dimensional quantum systems (KMS states) and the discovery of modular action as geometric transformations. However, our main focus are its applications in physics, in particular the modular action as Lorentz boosts on the Rindler wedge, as dilations on the forward light cone and as conformal mappings on the double cone. Subsequently, their most important implications in local quantum physics are discussed. The purpose of this thesis is to shed more light on the transition from the known massless modular action to the wanted massive one in the case of double cones. First of all the infinitesimal generator of the massive modular group is investigated, especially some assumptions on its structure are verified explicitly for the first time for two concrete examples. Then, two strategies for the calculation of group itself are discussed. Some formalisms and results from operator theory and the method of second quantisation used in this thesis are made available in the appendix.},
1734         author = {T. Saffary},
1735         eprint = {math-ph/0512046},
1736         localfile = {2005 - Saffary - Modular action on the massive algebra.pdf},
1737         slaccitation = {\%\%CITATION = MATH-PH/0512046\\;\%\%},
1738         title = {{Modular action on the massive algebra}},
1739         url = {http://arxiv.org/abs/math-ph/0512046},
1740         year = {2005}
1741 }
1742 
1743 @article{Salvitti:2007,
1744         abstract = {In the framework of algebraic quantum field theory we analyze the anomalous statistics exhibited by a class of automorphisms of the observable algebra of the two-dimensional free massive Dirac field, constructed by fermionic gauge group methods. The violation of Haag duality, the topological peculiarity of a two-dimensional space-time and the fact that unitary implementers do not lie in the global field algebra account for strange behaviour of statistics, which is no longer an intrinsic property of sectors. Since automorphisms are not inner, we exploit asymptotic abelianness of intertwiners in order to construct a braiding for a suitable $C^*$-tensor subcategory of End($\mathscr{A}$). We define two inequivalent classes of path connected bi-asymptopias, selecting only those sets of nets which yield a true generalized statistics operator.},
1745         author = {D. Salvitti},
1746         eprint = {hep-th/0507107},
1747         journal = {Commun. Math. Phys.},
1748         localfile = {2007 - Salvitti - Generalized particle statistics in two-dimensions: Examples from the theory of free massive Dirac field.pdf},
1749         pages = {473--492},
1750         slaccitation = {\%\%CITATION = HEP-TH/0507107\\;\%\%},
1751         title = {{Generalized particle statistics in two-dimensions: Examples from the theory of free massive Dirac field}},
1752         url = {http://arxiv.org/abs/hep-th/0507107},
1753         volume = {269},
1754         year = {2007}
1755 }
1756 
1757 @article{Schroer:2005-1,
1758         abstract = {The recent concept of modular localization of wedge algebras suggests two methods of classifying and constructing QFTs, one based on particle-like generators of wedge algebras using on-shell concepts (S-matrix, formfactors. crossing property) and the other using the off-shell simplification of lightfront holography (chiral theories). The lack of an operator interpretation of the crossing property is a serious obstacle in on-shell constructions. In special cases one can define a ``masterfield'' whose connected formfactors constitute an auxiliary thermal QFT for which the KMS cyclicity equation is identical to the crossing property of the formfactors of the master field. Further progress is expected to result from a conceptual understanding of the role of on-shell concepts as particle states and the S-matrix within the holographic lightfront projection.},
1759         author = {B. Schroer},
1760         eprint = {hep-th/0406016},
1761         journal = {Ann. Phys.},
1762         localfile = {2005 - Schroer - Constructive proposals for QFT based on the crossing property and on lightfront holography.pdf},
1763         pages = {48--91},
1764         slaccitation = {\%\%CITATION = HEP-TH/0406016\\;\%\%},
1765         title = {{Constructive proposals for QFT based on the crossing property and on lightfront holography}},
1766         url = {http://arxiv.org/abs/hep-th/0406016},
1767         volume = {319},
1768         year = {2005}
1769 }
1770 
1771 @article{BahnsWaldmann:2007,
1772         abstract = {Localized noncommutative structures for manifolds with connection are constructed based on the use of vertical star products. The model's main feature is that two points that are far away from each other will not be subject to a deviation from classical geometry while space-time becomes noncommutative for pairs of points that are close to one another.},
1773         author = {D. Bahns and S. Waldmann},
1774         eprint = {math/0607745},
1775         journal = {Rev. Math. Phys.},
1776         keywords = {NCQFT; kw:local-ncqft},
1777         localfile = {2006 - Bahns, Waldmann - Locally Noncommutative Space-Times.pdf},
1778         pages = {273--306},
1779         slaccitation = {\%\%CITATION = MATH/0607745\\;\%\%},
1780         title = {{Locally Noncommutative Space-Times}},
1781         url = {http://arxiv.org/abs/math/0607745},
1782         volume = {19},
1783         year = {2007}
1784 }
1785 
1786 @article{BalachandranGovindarajanManganoPinzulQureshiVaidya:2007,
1787         abstract = {We elaborate on the role of quantum statistics in twisted Poincare invariant theories. It is shown that, in order to have twisted Poincare group as the symmetry of a quantum theory, statistics must be twisted. It is also confirmed that the removal of UV-IR mixing (in the absence of gauge fields) in such theories is a natural consequence.},
1788         author = {A. P. Balachandran and T. R. Govindarajan and G. Mangano and A. Pinzul and B. A. Qureshi and S. Vaidya},
1789         eprint = {hep-th/0608179},
1790         journal = {Phys. Rev.},
1791         keywords = {NCQFT},
1792         localfile = {2006 - Balachandran, Govindarajan, Mangano, Pinzul, Qureshi, Vaidya - Statistics and UV-IR Mixing with Twisted Poincare Invariance.pdf},
1793         pages = {045009},
1794         slaccitation = {\%\%CITATION = HEP-TH/0608179\\;\%\%},
1795         title = {{Statistics and UV-IR mixing with twisted Poincare invariance}},
1796         url = {http://arxiv.org/abs/hep-th/0608179},
1797         volume = {D75},
1798         year = {2007}
1799 }
1800 
1801 @article{BalachandranPinzulQureshiVaidya:2006,
1802         abstract = {Recent work indicates an approach to the formulation of diffeomorphism invariant quantum field theories (qft's) on the Groenewold-Moyal (GM) plane. In this approach to the qft's, statistics gets twisted and the S-matrix in the non-gauge qft's become independent of the noncommutativity parameter \theta^{\mu \nu}. Here we show that the noncommutative algebra has a commutative spacetime algebra as a substructure: the Poincar\'{e} and diffeomorphism groups are based on this algebra in the twisted approach. It is natural to preserve gauge symmetries as well by basing it on this algebra. Then gravity and gauge sectors are the same those for \theta^{\mu \nu}=0, but their interaction with matter fields is sensitive to \theta^{\mu \nu}. We calculate e^- + e^- -\&gt; e^- + e^- and \gamma + e^- \-\&gt; \gamma + e^- cross-sections in the tree approximation and explicitly display their dependence on \theta^{\mu \nu}. Remarkably the zero of the elastic e^- + e^-\ -\&gt; e^- + e^- cross-section at 90-degrees in the centre-of-mass system, which is due to Pauli principle, is shifted away as a function of \theta^{\mu \nu} and energy. This shows that noncommutativity modifies Pauli principle. We study this motion of zero in detail. An important final point of this paper is the following: the S-matrix involves time-ordered products of the interaction Hamiltonian densit\y H\_I, a\nd H\_I(x) \and H\_I(y) do not commute when x and y are space-like separated. As a result, the S-matrix is not Lorentz-invariant despite the preceding efforts to maintain it.},
1803         author = {A. P. Balachandran and A. Pinzul and B. A. Qureshi and S. Vaidya},
1804         eprint = {hep-th/0608138},
1805         keywords = {NCQFT},
1806         localfile = {2006 - Balachandran, Pinzul, Qureshi, Vaidya - Poincare Invariant Gauge and Gravity Theories on the Groenewold-Moyal Plane.pdf},
1807         slaccitation = {\%\%CITATION = HEP-TH/0608138\\;\%\%},
1808         title = {{Poincare invariant gauge and gravity theories on the Groenewold-Moyal plane}},
1809         url = {http://arxiv.org/abs/hep-th/0608138},
1810         year = {2006}
1811 }
1812 
1813 @article{BuchholzSchlemmer:2007,
1814         abstract = {A physically meaningful local concept of temperature is introduced in quantum field theory on curved spacetime and applied to the example of a massless field on de Sitter space. It turns out in this model that the equilibrium (Gibbs) states which can be prepared by a geodesic observer have in general a varying temperature distribution in the neighborhood of the geodesic and may not even allow for a consistent thermal interpretation close to the horizon. This result, which can be traced back to the Unruh effect, illustrates the failure of a global notion of temperature in curved spacetime and reveals the need for a local concept, as presented here.},
1815         author = {D. Buchholz and J. Schlemmer},
1816         eprint = {gr-qc/0608133},
1817         journal = {Class. Quant. Grav.},
1818         localfile = {2006 - Buchholz, Schlemmer - Local Temperature in Curved Spacetime.pdf},
1819         pages = {F25},
1820         slaccitation = {\%\%CITATION = GR-QC/0608133\\;\%\%},
1821         title = {{Local temperature in curved spacetime}},
1822         url = {http://arxiv.org/abs/gr-qc/0608133},
1823         volume = {24},
1824         year = {2007}
1825 }
1826 
1827 @article{BytskoTeschner:2006,
1828         abstract = {We define and study certain integrable lattice models with non-compact quantum group symmetry (the modular double of U\_q(s\l\_2)) including an integrable lattice regularization of the sinh-Gordon model and a non-compact version of the XXZ model. Their fundamental R-matrices are constructed in terms of the non-compact quantum dilogarithm. Our choice of the quantum group representations naturally ensures self-adjointness of the Hamiltonian and the higher integrals of motion. These models are studied with the help of the separation of variables method. We show that the spectral problem for the integrals of motion can be reformulated as the problem to determine a subset among the solutions to certain finite difference equations (Baxter equation and quantum Wronskian equation) which is characterized by suitable analytic and asymptotic properties. A key technical tool is the so-called Q-operator, for which we give an explicit construction. Our results allow us to establish some connections to related results and conjectures on the sinh-Gordon theory in continuous space-time. Our approach also sheds some light on the relations between massive and massless models (in particular, the sinh-Gordon and Liouville theories) from the point of view of their integrable structures.},
1829         author = {A. G. Bytsko and J. Teschner},
1830         eprint = {hep-th/0602093},
1831         journal = {J. Phys.},
1832         localfile = {2006 - Bytsko, Teschner - Quantization of models with non-compact quantum group symmetry: Modular XXZ magnet and lattice sinh-Gordon model.pdf},
1833         pages = {12927--12981},
1834         slaccitation = {\%\%CITATION = HEP-TH/0602093\\;\%\%},
1835         title = {{Quantization of models with non-compact quantum group symmetry: Modular XXZ magnet and lattice sinh-Gordon model}},
1836         url = {http://arxiv.org/abs/hep-th/0602093},
1837         volume = {A39},
1838         year = {2006}
1839 }
1840 
1841 @article{FewsterPfenning:2006,
1842         abstract = {We begin a systematic study of Quantum Energy Inequalities (QEIs) in relation to local covariance. We define notions of locally covariant QEIs of both 'absolute' and 'difference' types and show that existing QEIs satisfy these conditions. Local covariance permits us to place constraints on the renormalised stress-energy tensor in one spacetime using QEIs derived in another, in subregions where the two spacetimes are isometric. This is of particular utility where one of the two spacetimes exhibits a high degree of symmetry and the QEIs are available in simple closed form. Various general applications are presented, including a priori constraints (depending only on geometric quantities) on the ground-state energy density in a static spacetime containing locally Minkowskian regions. In addition, we present a number of concrete calculations in both two and four dimensions which demonstrate the consistency of our bounds with various known ground- and thermal state energy densities. Examples considered include the Rindler and Misner spacetimes, and spacetimes with toroidal spatial sections. In this paper we confine the discussion to globally hyperbolic spacetimes; subsequent papers will also discuss spacetimes with boundary and other related issues.},
1843         author = {C. J. Fewster and M. J. Pfenning},
1844         eprint = {math-ph/0602042},
1845         journal = {J. Math. Phys.},
1846         localfile = {2006 - Fewster, Pfenning - Quantum energy inequalities and local covariance. I: Globally hyperbolic spacetimes.pdf},
1847         pages = {082303},
1848         slaccitation = {\%\%CITATION = MATH-PH/0602042\\;\%\%},
1849         title = {{Quantum energy inequalities and local covariance. I: Globally hyperbolic spacetimes}},
1850         url = {http://arxiv.org/abs/math-ph/0602042},
1851         volume = {47},
1852         year = {2006}
1853 }
1854 
1855 @article{Fleischhack:2005,
1856         abstract = {We present a construction method for mappings between generalized connections, comprising, e.g., the action of gauge transformations, diffeomorphisms and Weyl transformations. Moreover, criteria for continuity and measure preservation are stated.},
1857         author = {C. Fleischhack},
1858         eprint = {math-ph/0601005},
1859         localfile = {2005 - Fleischhack - Construction of generalized connections.pdf},
1860         slaccitation = {\%\%CITATION = MATH-PH/0601005\\;\%\%},
1861         title = {{Construction of generalized connections}},
1862         url = {http://arxiv.org/abs/math-ph/0601005},
1863         year = {2005}
1864 }
1865 
1866 @article{Fleischhack:2004-1,
1867         abstract = {The Weyl algebra A of continuous functions and exponentiated fluxes, introduced by Ashtekar, Lewandowski and others, in quantum geometry is studied. It is shown that, in the piecewise analytic category, every regular representation of A having a cyclic and diffeomorphism invariant vector, is already unitarily equivalent to the fundamental representation. Additional assumptions concern the dimension of the underlying analytic manifold (at least three), the finite wide triangulizability of surfaces in it to be used for the fluxes and the naturality of the action of diffeomorphisms -- but neither any domain properties of the represented Weyl operators nor the requirement that the diffeomorphisms act by pull-backs. For this, the general behaviour of C*-algebras generated by continuous functions and pull-backs of homeomorphisms, as well as the properties of stratified analytic diffeomorphisms are studied. Additionally, the paper includes also a short and direct proof of the irreducibility of A.},
1868         author = {C. Fleischhack},
1869         eprint = {math-ph/0407006},
1870         localfile = {2004 - Fleischhack - Representations of the Weyl algebra in quantum geometry.pdf},
1871         slaccitation = {\%\%CITATION = MATH-PH/0407006\\;\%\%},
1872         title = {{Representations of the Weyl algebra in quantum geometry}},
1873         url = {http://arxiv.org/abs/math-ph/0407006},
1874         year = {2004}
1875 }
1876 
1877 @article{WreszinskiJkel:2006,
1878         abstract = {We consider the formal non relativistc limit (nrl) of the :\phi^4:\_{s+1} relativistic quantum field theory (rqft), where s is the space dimension. Following work of R. Jackiw, we show that, for s=2 and a given value of the ultraviolet cutoff \kappa, there are two ways to perform the nrl: i.) fixing the renormalized mass m^2 equal to the bare mass \m\_0^2; ii.) keeping the renormalized mass fixed and different from the bare mass\ m\_0^2. In the (infinite-volume) two-particle sector the scattering amplitude tends to zero as \kapp\a -\&gt; \infty in case i.) and, in case ii.), there is a bound state, indicating that the interaction potential is attractive. As a consequence, stability of matter fails for our boson system. We discuss why both alternatives do not reproduce the low-energy behaviour of the full rqft. The singular nature of the nrl is also nicely illustrated for s=1 by a rigorous stability/instability result of a different nature.},
1879         author = {W. F. Wreszinski and C. D. J{\"{a}}kel},
1880         eprint = {math-ph/0609059},
1881         localfile = {2006 - J\"{a}kel, Wreszinski - Stability and related properties of vacua and ground states.pdf},
1882         slaccitation = {\%\%CITATION = MATH-PH/0609059\\;\%\%},
1883         title = {{Stability and related properties of vacua and ground states}},
1884         url = {http://arxiv.org/abs/math-ph/0609059},
1885         year = {2006}
1886 }
1887 
1888 @article{Kulish:2006,
1889         abstract = {The role of quantum universal enveloping algebras of symmetries in constructing a noncommutative geometry of space-time and corresponding field theory is discussed. It is shown that in the framework of the twist theory of quantum groups, the noncommutative (super) space-time defined by coordinates with Heisenberg commutation relations, is (super) Poincar\'{e} invariant, as well as the corresponding field theory. Noncommutative parameters of global transformations are introduced.},
1890         author = {P. P. Kulish},
1891         eprint = {hep-th/0606056},
1892         localfile = {2006 - Kulish - Twists of quantum groups and noncommutative field theory.pdf},
1893         slaccitation = {\%\%CITATION = HEP-TH/0606056\\;\%\%},
1894         title = {{Twists of quantum groups and noncommutative field theory}},
1895         url = {http://arxiv.org/abs/hep-th/0606056},
1896         year = {2006}
1897 }
1898 
1899 @article{LewandowskiOkolowSahlmannThiemann:2005,
1900         abstract = {Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic kinematical observables and represents it through operators on a suitable Hilbert space. In a second step, one implements the constraints. The main result of the paper concerns the representation theory of the kinematical algebra: We show that there is only one cyclic representation invariant under spatial diffeomorphisms. While this result is particularly important for loop quantum gravity, we are rather general: The precise definition of the abstract *-algebra of the basic kinematical observables we give could be used for any theory in which the configuration variable is a connection with a compact structure group. The variables are constructed from the holonomy map and from the fluxes of the momentum conjugate to the connection. The uniqueness result is relevant for any such theory invariant under spatial diffeomorphisms or being a part of a diffeomorphism invariant theory.},
1901         author = {J. Lewandowski and A. Okolow and H. Sahlmann and T. Thiemann},
1902         eprint = {gr-qc/0504147},
1903         localfile = {2005 - Lewandowski, Okolow, Sahlmann - Uniqueness of diffeomorphism invariant states on holonomy- flux algebras.pdf},
1904         slaccitation = {\%\%CITATION = GR-QC/0504147\\;\%\%},
1905         title = {{Uniqueness of diffeomorphism invariant states on holonomy- flux algebras}},
1906         url = {http://arxiv.org/abs/gr-qc/0504147},
1907         year = {2005}
1908 }
1909 
1910 @article{Zahn:2006,
1911         abstract = {We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the twisted structure is so rigid that it is hard to derive any predictions, unless one gives up general principles of quantum theory. It is also shown that the twisted structure is not responsible for the presence or absence of UV/IR-mixing, as claimed in the literature.},
1912         author = {J. Zahn},
1913         eprint = {hep-th/0603231},
1914         journal = {Phys. Rev.},
1915         localfile = {2006 - Zahn - Remarks on twisted noncommutative quantum field theory.pdf},
1916         pages = {105005},
1917         slaccitation = {\%\%CITATION = HEP-TH/0603231\\;\%\%},
1918         title = {{Remarks on twisted noncommutative quantum field theory}},
1919         url = {http://arxiv.org/abs/hep-th/0603231},
1920         volume = {D73},
1921         year = {2006}
1922 }
1923 
1924 @article{BergbauerKreimer:2007,
1925         abstract = {In this expository article we review recent advances in our understanding of the combinatorial and algebraic structure of perturbation theory in terms of Feynman graphs, and Dyson-Schwinger equations. Starting from Lie and Hopf algebras of Feynman graphs, perturbative renormalization is rephrased algebraically. The Hochschild cohomology of these Hopf algebras leads the way to Slavnov-Taylor identities and Dyson-Schwinger equations. We discuss recent progress in solving simple Dyson-Schwinger equations in the high energy sector using the algebraic machinery. Finally there is a short account on a relation to algebraic geometry and number theory: understanding Feynman integrals as periods of mixed (Tate) motives.},
1926         author = {C. Bergbauer and D. Kreimer},
1927         eprint = {arXiv:0704.0232 [hep-th]},
1928         localfile = {2007 - Bergbauer, Kreimer - New Algebraic Aspects of Perturbative and Non-Perturbative Quantum Field Theory.pdf},
1929         slaccitation = {\%\%CITATION = ARXIV:0704.0232\\;\%\%},
1930         title = {{New algebraic aspects of perturbative and non-perturbative Quantum Field Theory}},
1931         url = {http://arxiv.org/abs/0704.0232},
1932         year = {2007}
1933 }
1934 
1935 @article{BrunettiGuidoLongo:2002,
1936         abstract = {We propose a framework for the free field construction of algebras of local observables which uses as an input the Bisognano-Wichmann relations and a representation of the Poincare' group on the one-particle Hilbert space. The abstract real Hilbert subspace version of the Tomita-Takesaki theory enables us to bypass some limitations of the Wigner formalism by introducing an intrinsic spacetime localization. Our approach works also for continuous spin representations to which we associate a net of von Neumann algebras on spacelike cones with the Reeh-Schlieder property. The positivity of the energy in the representation turns out to be equivalent to the isotony of the net, in the spirit of Borchers theorem. Our procedure extends to other spacetimes homogeneous under a group of geometric transformations as in the case of conformal symmetries and de Sitter spacetime.},
1937         author = {R. Brunetti and D. Guido and R. Longo},
1938         doi = {10.1142/S0129055X02001387},
1939         eprint = {math-ph/0203021},
1940         journal = {Rev. Math. Phys.},
1941         localfile = {2002 - Brunetti, Guido, Longo - Modular localization and Wigner particles.pdf},
1942         pages = {759--786},
1943         slaccitation = {\%\%CITATION = MATH-PH/0203021\\;\%\%},
1944         title = {{Modular localization and Wigner particles}},
1945         url = {http://arxiv.org/abs/math-ph/0203021},
1946         volume = {14},
1947         year = {2002}
1948 }
1949 
1950 @article{BuchholzGrundling:2007,
1951         abstract = {The standard C*-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does it incorporate pertinent physical observables such as (bounded functions of) the Hamiltonian. Here a novel C*-algebra of the canonical commutation relations is presented which does not suffer from such problems. It is based on the resolvents of the canonical operators and their algebraic relations. The resulting C*-algebra, the resolvent algebra, is shown to have many desirable analytic properties and the regularity structure of its representations is surprisingly simple. Moreover, the resolvent algebra is a convenient framework for applications to interacting and to constrained quantum systems, as we demonstrate by several examples.},
1952         author = {D. Buchholz and H. Grundling},
1953         eprint = {arXiv:0705.1988 [math.OA]},
1954         localfile = {2007 - Buchholz, Grundling - The resolvent algebra: A new approach to canonical quantum systems.pdf},
1955         slaccitation = {\%\%CITATION = ARXIV:0705.1988\\;\%\%},
1956         title = {{The resolvent algebra: A new approach to canonical quantum systems}},
1957         url = {http://arxiv.org/abs/0705.1988},
1958         year = {2007}
1959 }
1960 
1961 @article{BuchholzLongo:1999,
1962         abstract = {It is shown that the modulus of any graded or, more generally, twisted KMS functional of a C*-dynamical system is proportional to an ordinary KMS state and the twist is weakly inner in the corresponding GNS-representation. If the functional is invariant under the adjoint action of some asymptotically abelian family of automorphisms, then the twist is trivial. As a consequence, such functionals do not exist for supersymmetric C*-dynamical systems. This is in contrast with the situation in compact spaces where super KMS functionals occur as super-Gibbs functionals.},
1963         author = {D. Buchholz and R. Longo},
1964         eprint = {hep-th/9905102},
1965         journal = {Adv. Theor. Math. Phys.},
1966         localfile = {2000 - Buchholz, Longo - Graded KMS Functionals and the Breakdown of Supersymmetry.pdf},
1967         pages = {615--626},
1968         slaccitation = {\%\%CITATION = HEP-TH/9905102\\;\%\%},
1969         title = {{Graded KMS functionals and the breakdown of supersymmetry}},
1970         url = {http://arxiv.org/abs/hep-th/9905102},
1971         volume = {3},
1972         year = {1999}
1973 }
1974 
1975 @article{Fewster:2006,
1976         abstract = {We formulate Quantum Energy Inequalities (QEIs) in the framework of locally covariant quantum field theory developed by Brunetti, Fredenhagen and Verch, which is based on notions taken from category theory. This leads to a new viewpoint on the QEIs, and also to the identification of a new structural property of locally covariant quantum field theory, which we call Local Physical Equivalence. Covariant formulations of the numerical range and spectrum of locally covariant fields are given and investigated, and a new algebra of fields is identified, in which fields are treated independently of their realisation on particular spacetimes and manifestly covariant versions of the functional calculus may be formulated.},
1977         author = {C. J. Fewster},
1978         eprint = {math-ph/0611058},
1979         localfile = {2006 - Fewster - Quantum energy inequalities and local covariance. II: Categorical formulation.pdf},
1980         slaccitation = {\%\%CITATION = MATH-PH/0611058\\;\%\%},
1981         title = {{Quantum energy inequalities and local covariance. II: Categorical formulation}},
1982         url = {http://arxiv.org/abs/math-ph/0611058},
1983         year = {2006}
1984 }
1985 
1986 @techreport{Fiore:2007,
1987         abstract = {We sketch a natural affirmative answer to the question based on a joint work [11] with J. Wess. There we argue that a proper enforcement of the ``twisted Poincare' '' covariance makes any differences $(x-y)^\mu$ of coordinates of two copies of the Moyal-Weyl deformation of Minkowski space like undeformed. Then QFT in an operator approach becomes compatible with (minimally adapted) Wightman axioms and time-ordered perturbation theory, and physically equivalent to ordinary QFT, as observables involve only coordinate differences.},
1988         author = {G. Fiore},
1989         keywords = {High Energy Physics - Theory (hep-th)},
1990         number = {Preprint 07-16 Dip. Matematica e Applicazioni, Universit\`{a} di Napoli; DSF/12-2007},
1991         pdf = {http://arxiv.org/pdf/0705.1120},
1992         title = {{Can QFT on Moyal-Weyl spaces look as on commutative ones?}},
1993         url = {http://arxiv.org/abs/0705.1120},
1994         v1descr = {Tue, 8 May 2007 16:11:31 GMT (11kb)},
1995         year = {2007}
1996 }
1997 
1998 @article{FioreWess:2007,
1999         abstract = {We explore some general consequences of a proper, full enforcement of the twisted Poincare'\" covariance of Chaichian et al. [14], Wess [50], Koch et al. [34], Oeckl [41] upon many-particle quantum mechanics and field quantization on a Moyal-Weyl noncommutative space(time). This entails the associated braided tensor product with an involutive braiding (or $\star$-tensor product in the parlance of Aschieri et al. [3,4]) prescription for any coordinates pair of $x,y$ generating two different copies of the space(time); the associated nontrivial commutation relations between them imply that $x-y$ is central and its Poincare transformation properties remain undeformed. As a consequence, in QFT (even with space-time noncommutativity) one can reproduce notions (like space-like separation, time- and normal-ordering, Wightman or Green's functions, etc), impose constraints (Wightman axioms), and construct free or interacting theories which essentially coincide with the undeformed ones, since the only observable quantities involve coordinate differences. In other words, one may thus well realize QM and QFT's where the effect of space(time) noncommutativity amounts to a practically unobservable common noncommutative translation of all reference frames.},
2000         author = {G. Fiore and J. Wess},
2001         eprint = {hep-th/0701078},
2002         journal = {Phys. Rev.},
2003         keywords = {NCQFT},
2004         localfile = {2007 - Fiore, Wess - On full twisted Poincare' symmetry and QFT on Moyal-Weyl spaces.pdf},
2005         pages = {105022},
2006         slaccitation = {\%\%CITATION = HEP-TH/0701078\\;\%\%},
2007         title = {{On 'full' twisted {P}oincare' symmetry and {QFT} on {M}oyal-{W}eyl spaces}},
2008         url = {http://arxiv.org/abs/hep-th/0701078},
2009         volume = {D75},
2010         year = {2007}
2011 }
2012 
2013 @article{GuidoLongoWiesbrock:1998,
2014         abstract = {Starting with a conformal Quantum Field Theory on the real line, we show that the dual net is still conformal with respect to a new representation of the Moebius group. We infer from this that every conformal net is normal and conormal, namely the local von Neumann algebra associated with an interval coincides with its double relative commutant inside the local von Neumann algebra associated with any larger interval. The net and the dual net give together rise to an infinite dimensional symmetry group, of which we study a class of positive energy irreducible representations. We mention how superselsection sectors extend to the dual net and we illustrate by examples how, in general, this process generates solitonic sectors. We describe the free theories associated with the lowest weight n representations of PSL(2,R), showing that they violate 3-regularity for n\&gt;2. When \n\&gt;1, we obtain examples of non Moebius-covariant sectors of a 3-regular (non 4-regular) net.},
2015         author = {D. Guido and R. Longo and H.W. Wiesbrock},
2016         eprint = {hep-th/9703129},
2017         journal = {Commun. Math. Phys.},
2018         localfile = {1998 - Guido, Longo, Wiesbrock - Extensions of Conformal Nets and Superselection Structures.pdf},
2019         pages = {217--244},
2020         slaccitation = {\%\%CITATION = HEP-TH/9703129\\;\%\%},
2021         title = {{Extensions of conformal nets and superselection structures}},
2022         url = {http://arxiv.org/abs/hep-th/9703129},
2023         volume = {192},
2024         year = {1998}
2025 }
2026 
2027 @article{Hlzler:2007,
2028         abstract = {A unified treatment of Schwinger parametrised Feynman amplitudes is suggested which addresses vertices of arbitrary order on the same footing as propagators. Contributions from distinct diagrams are organised collectively. The scheme is based on the continuous graph Laplacian. The analogy to a classical statistical diffusion system of vector charges on the graph is explored.},
2029         author = {H. H{\"{o}}lzler},
2030         journal = {JHEP},
2031         keywords = {High Energy Physics - Theory (hep-th)},
2032         pages = {022},
2033         pdf = {http://arxiv.org/pdf/0704.3392},
2034         title = {{World Graph Formalism for Feynman Amplitudes}},
2035         url = {http://arxiv.org/abs/0704.3392},
2036         v1descr = {Wed, 25 Apr 2007 15:14:42 GMT (58kb)},
2037         v1url = {http://www.arxiv.org/abs/0704.3392v1},
2038         v2descr = {Thu, 26 Apr 2007 08:09:05 GMT (58kb)},
2039         v2url = {http://www.arxiv.org/abs/0704.3392v2},
2040         v3descr = {Mon, 21 Apr 2008 22:28:48 GMT (62kb)},
2041         v3url = {http://www.arxiv.org/abs/0704.3392v3},
2042         v4descr = {Tue, 19 Aug 2008 20:46:22 GMT (63kb)},
2043         volume = {0809},
2044         year = {2008}
2045 }
2046 
2047 @phdthesis{Lechner:2006,
2048         abstract = {The subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two-dimensional Minkowski space. The input in this construction is not a classical Lagrangian, but rather a prescribed factorizing S-matrix, i.e. the inverse scattering problem for such quantum field theories is studied. For a large class of factorizing S-matrices, certain associated quantum fields, which are localized in wedge-shaped regions of Minkowski space, are constructed explicitely. With the help of these fields, the local observable content of the corresponding model is defined and analyzed by employing methods from the algebraic framework of quantum field theory. The abstract problem in this analysis amounts to the question under which conditions an algebra of wedge-localized observables can be used to generate a net of local observable algebras with the right physical properties. The answer given here uses the so-called modular nuclearity condition, which is shown to imply the existence of local observables and the Reeh-Schlieder property. In the analysis of the concrete models, this condition is proven for a large family of S-matrices, including the scattering operators of the Sinh-Gordon model and the scaling Ising model as special examples. The so constructed models are then investigated with respect to their scattering properties. They are shown to solve the inverse scattering problem for the considered S-matrices, and a proof of asymptotic completeness is given.},
2049         author = {G. Lechner},
2050         eprint = {math-ph/0611050},
2051         journal = {PhDThesis},
2052         localfile = {2006 - Lechner - On the Construction of Quantum Field Theories with Factorizing S-Matrices-PhD-Thesis.pdf},
2053         school = {University of G\"{o}ttingen},
2054         slaccitation = {\%\%CITATION = MATH-PH/0611050\\;\%\%},
2055         title = {{On the construction of quantum field theories with factorizing S-matrices}},
2056         url = {http://arxiv.org/abs/math-ph/0611050},
2057         x-color = {#199bff},
2058         year = {2006}
2059 }
2060 
2061 @article{Lorenzen:2007,
2062         author = {R. Lorenzen},
2063         localfile = {2007 - Lorenzen - From Spin Groups and Modular P_1CT Symmetry to Covariant Representations and the Spin-Statistics Theorem.pdf},
2064         note = {DESY-THESIS-2007-009},
2065         title = {{From spin groups and modular P(1)CT symmetry to covariant representations and the spin-statistics theorem}},
2066         year = {2007}
2067 }
2068 
2069 @article{Olbermann:2007,
2070         abstract = {We construct a new class of physical states of the free Klein-Gordon field in Robertson-Walker spacetimes. This is done by minimizing the expectation value of smeared stress-energy. We get an explicit expression for the state depending on the smearing function. We call it a state of low energy. States of low energy are an improvement of the concept of adiabatic vacua on Robertson-Walker spacetimes. The latter are approximations of the former. It is shown that states of low energy are Hadamard states.},
2071         author = {H. Olbermann},
2072         journal = {Class.Quant.Grav.},
2073         keywords = {General Relativity and Quantum Cosmology (gr-qc)},
2074         pages = {5011--5030},
2075         pdf = {http://arxiv.org/pdf/0704.2986},
2076         title = {{States of Low Energy on Robertson-Walker Spacetimes}},
2077         url = {http://arxiv.org/abs/0704.2986},
2078         v1descr = {Mon, 23 Apr 2007 14:53:42 GMT (22kb)},
2079         v1url = {http://www.arxiv.org/abs/0704.2986v1},
2080         v2descr = {Mon, 30 Apr 2007 14:01:09 GMT (22kb)},
2081         volume = {24},
2082         year = {2007}
2083 }
2084 
2085 @misc{Schlemmer:2007,
2086         abstract = {In the framework of local thermodynamic equilibrium by Buchholz, Ojima and Roos, a class S\_x of observables, whose members are supposed to model idealized measurements of thermal properties of given states at spacetime points x, plays a crucial role in determining and characterizing local equilibrium states in quantum field theory. Here it will be shown how elements from this space can be reproduced by a specific model of the idealized measurements modeled by an Unruh-de Witt detector.},
2087         author = {J. Schlemmer},
2088         keywords = {High Energy Physics - Theory (hep-th)},
2089         localfile = {2007 - Schlemmer - Local Thermal Equilibrium States and Unruh Detectors in Quantum Field Theory.pdf},
2090         month = feb,
2091         pdf = {http://arxiv.org/pdf/hep-th/0702096},
2092         title = {{Local Thermal Equilibrium States and Unruh Detectors in Quantum Field Theory}},
2093         url = {http://arxiv.org/abs/hep-th/0702096},
2094         v1descr = {Tue, 13 Feb 2007 10:29:55 GMT (11kb)},
2095         year = {2007}
2096 }
2097 
2098 @phdthesis{Weiner:2007,
2099         abstract = {This PhD thesis focuses on local conformal nets of von Neumann algebras on the circle. For a more detailed description of its content and of the results published within, see its preface.},
2100         author = {M. Weiner},
2101         keywords = {Functional Analysis (math.FA); Mathematical Physics (math-ph); Operator Algebras (math.OA)},
2102         pdf = {http://arxiv.org/pdf/math/0703336},
2103         title = {{Conformal covariance and related properties of chiral QFT}},
2104         url = {http://arxiv.org/abs/math/0703336},
2105         v1descr = {Mon, 12 Mar 2007 12:24:11 GMT (127kb)},
2106         year = {2007}
2107 }
2108 
2109 @article{CarpiWeiner:2005,
2110         abstract = {A Moebius covariant net of von Neumann algebras on S^1 is diffeomorphism covariant if its Moebius symmetry extends to diffeomorphism symmetry. We prove that in case the net is either a Virasoro net or any at least 4-regular net such an extension is unique: the local algebras together with the Moebius symmetry (equivalently: the local algebras together with the vacuum vector) completely determine it. We draw the two following conclusions for such theories. (1) The value of the central charge c is an invariant and hence the Virasoro nets for different values of c are not isomorphic as Moebius covariant nets. (2) A vacuum preserving internal symmetry always commutes with the diffeomorphism symmetries. We further use our result to give a large class of new examples of nets (even strongly additive ones), which are not diffeomorphism covariant; i.e. which do not admit an extension of the symmetry to Diff^+(S^1).},
2111         author = {S. Carpi and M. Weiner},
2112         eprint = {math/0407190},
2113         journal = {Commun. Math. Phys.},
2114         localfile = {2005 - Carpi, Weiner - On the uniqueness of diffeomorphism symmetry in conformal field theory.pdf},
2115         pages = {203--221},
2116         slaccitation = {\%\%CITATION = MATH/0407190\\;\%\%},
2117         title = {{On the uniqueness of diffeomorphism symmetry in conformal field theory}},
2118         url = {http://arxiv.org/abs/math/0407190},
2119         volume = {258},
2120         year = {2005}
2121 }
2122 
2123 @article{CarpiKawahigashiLongo:2007,
2124         abstract = {We study the general structure of Fermi conformal nets of von Neumann algebras on the circle, consider a class of topological representations, the general representations, that we characterize as Neveu-Schwarz or Ramond representations, in particular a Jones index can be associated with each of them. We then consider a supersymmetric general representation associated with a Fermi modular net and give a formula involving the Fredholm index of the supercharge operator and the Jones index. We then consider the net associated with the super-Virasoro algebra and discuss its structure. If the central charge c belongs to the discrete series, this net is modular by the work of F. Xu and we get an example where our setting is verified by considering the Ramond irreducible representation with lowest weight c/24. We classify all the irreducible Fermi extensions of any super-Virasoro net in the discrete series, thus providing a classification of all superconformal nets with central charge less than 3/2.},
2125         author = {S. Carpi and Y. Kawahigashi and R. Longo},
2126         journal = {Annales Henri Poincare},
2127         keywords = {Mathematical Physics (math-ph); Operator Algebras (math.OA)},
2128         localfile = {2007 - Carpi, Kawahigashi, Longo - Structure and Classification of Superconformal Nets.pdf},
2129         pages = {1069--1121},
2130         pdf = {http://arxiv.org/pdf/0705.3609},
2131         title = {{Structure and Classification of Superconformal Nets}},
2132         url = {http://arxiv.org/abs/0705.3609},
2133         v1descr = {Thu, 24 May 2007 16:15:15 GMT (45kb)},
2134         v1url = {http://www.arxiv.org/abs/0705.3609v1},
2135         v2descr = {Mon, 3 Mar 2008 18:07:21 GMT (48kb)},
2136         volume = {9},
2137         year = {2008}
2138 }
2139 
2140 @article{Pinamonti:2007,
2141         abstract = {Some years ago it was shown that, in some cases, a notion of locality can arise from the group of symmetry enjoyed by the theory, thus in an intrinsic way. In particular, when Moebius covariance is present, it is possible to associate some particular transformations to the Tomita Takesaki modular operator and conjugation of a specific interval of an abstract circle. In this context we propose a way to define an operator representing the coordinate conjugated with the modular transformations. Remarkably this coordinate turns out to be compatible with the abstract notion of locality. Finally a concrete example concerning a quantum particle on a line is also given.},
2142         author = {N. Pinamonti},
2143         eprint = {math-ph/0610070},
2144         journal = {Rev. Math. Phys.},
2145         localfile = {2007 - Pinamonti - On localization and position operators in Moebius covariant theories.pdf},
2146         pages = {385--404},
2147         slaccitation = {\%\%CITATION = MATH-PH/0610070\\;\%\%},
2148         title = {{On localization and position operators in Moebius covariant theories}},
2149         url = {http://arxiv.org/abs/math-ph/0610070},
2150         volume = {19},
2151         year = {2007}
2152 }
2153 
2154 @article{BalachandranPinzulQureshiVaidya:2007,
2155         abstract = {Twisted quantum field theories on the Groenewold-Moyal plane are known to be non-local. Despite this non-locality, it is possible to define a generalized notion of causality. We show that interacting quantum field theories that involve only couplings between matter fields, or between matter fields and minimally coupled U(1) gauge fields are causal in this sense. On the other hand, interactions between matter fields and non-abelian gauge fields violate this generalized causality. We derive the modified Feynman rules emergent from these features. They imply that interactions of matter with non-abelian gauge fields are not Lorentz- and CPT-invariant.},
2156         author = {A. P. Balachandran and A. Pinzul and B. A. Qureshi and S. Vaidya},
2157         journal = {Phys. Rev. D},
2158         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Lesen; Mathematical Physics (math-ph); NCQFT; Quantum Algebra (math.QA)},
2159         pages = {025020},
2160         pdf = {http://arxiv.org/pdf/0708.1379},
2161         title = {{S-Matrix on the Moyal Plane: Locality versus Lorentz Invariance}},
2162         url = {http://arxiv.org/abs/0708.1379},
2163         v1descr = {Fri, 10 Aug 2007 08:25:57 GMT (21kb)},
2164         v1url = {http://www.arxiv.org/abs/0708.1379v1},
2165         v2descr = {Thu, 16 Aug 2007 04:18:27 GMT (21kb)},
2166         volume = {77},
2167         year = {2008}
2168 }
2169 
2170 @article{KayLarkin:2007,
2171         abstract = {We construct a symplectic isomorphism, h, from classical Klein Gordon solutions of mass m on (d+1)-dimensional Lorentzian Anti de Sitter space (equipped with the usual symplectic form) to a certain symplectic space of functions on its conformal boundary (only) for all integer and half-integer Delta (= d/2 + (1/2)(d^2 + 4m^2)^{1/2}). h induces a large family of new examples of Rehren's algebraic holography in which the net of local quantum Klein Gordon algebras in AdS is seen to map to a suitably defined net of local algebras for the (generalized free) scalar conformal field with anomalous dimension Delta on d-dimensional Minkowski space (the AdS boundary). Relatedly, we show for these models that Bertola et al's boundary-limit holography becomes a quantum duality (only) if the test functions for boundary Wightman distributions are restricted in a particular way.},
2172         author = {Bernard S. Kay and Peter Larkin},
2173         journal = {Phys. Rev. D},
2174         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
2175         pages = {121501},
2176         pdf = {http://arxiv.org/pdf/0708.1283},
2177         title = {{Pre-Holography}},
2178         url = {http://arxiv.org/abs/0708.1283},
2179         v1descr = {Thu, 9 Aug 2007 14:09:25 GMT (16kb)},
2180         v1url = {http://www.arxiv.org/abs/0708.1283v1},
2181         v2descr = {Mon, 10 Sep 2007 18:34:05 GMT (17kb)},
2182         v2url = {http://www.arxiv.org/abs/0708.1283v2},
2183         v3descr = {Fri, 16 May 2008 16:41:16 GMT (19kb)},
2184         volume = {77},
2185         year = {2008}
2186 }
2187 
2188 @article{BrosMoschella:2003,
2189         abstract = {We prove a Cauchy-type integral representation for classes of functions holomorphic in four priviledged tuboid domains of the complexified one-sheeted two-dimensional hyperboloid. From a physical viewpoint, this hyperboloid can be used for describing both the two-dimensional de Sitter and anti-de Sitter universes. For two of these tuboids, called ``the Lorentz tuboids'' and relevant for de Sitter Quantum Field Theory, the boundary values onto the real hyperboloid of functions holomorphic in these domains admit continuous Fourier-Helgason-type transforms. For the other two tuboids, called the ``chiral tuboids'' and relevant for anti-de Sitter Quantum Field Theory, the boundary values on the reals of functions holomorphic in these domains admit discrete Fourier-Helgason-type transforms. In both cases, the inversion formulae for these transformations are derived by using the previous Cauchy representation for the respective classes of functions. The decomposition of functions on the real hyperboloid into sums of boundary values of holomorphic functions from the previous four tuboids gives a complete and explicit treatment of the Gelfand-Gindikin program for the one-sheeted hyperboloid.},
2190         author = {J. Bros and U. Moschella},
2191         eprint = {math-ph/0311052},
2192         localfile = {2003 - Bros, Moschella - Fourier analysis and holomorphic decomposition on the one- sheeted hyperboloid.pdf},
2193         slaccitation = {\%\%CITATION = MATH-PH/0311052\\;\%\%},
2194         title = {{Fourier analysis and holomorphic decomposition on the one- sheeted hyperboloid}},
2195         url = {http://arxiv.org/abs/math-ph/0311052},
2196         year = {2003}
2197 }
2198 
2199 @article{BertolaCorbettaMoschella:2006,
2200         abstract = {We study the massless minimally coupled scalar field on a two--dimensional de Sitter space-time in the setting of axiomatic quantum field theory. We construct the invariant Wightman distribution obtained as the renormalized zero--mass limit of the massive one. Insisting on gauge invariance of the model we construct a vacuum state and a Hilbert space of physical states which are invariant under the action of the whole de Sitter group. We also present the integral expression of the conserved charge which generates the gauge invariance and propose a definition of dual field.},
2201         author = {M. Bertola and F. Corbetta and U. Moschella},
2202         eprint = {math-ph/0609080},
2203         localfile = {2006 - Bertola, Corbetta, Moschella - Massless scalar field in two-dimensional de Sitter universe.pdf},
2204         slaccitation = {\%\%CITATION = MATH-PH/0609080\\;\%\%},
2205         title = {{Massless scalar field in two-dimensional de Sitter universe}},
2206         url = {http://arxiv.org/abs/math-ph/0609080},
2207         year = {2006}
2208 }
2209 
2210 @article{BrosMoschella:1996,
2211         abstract = {We present a theory of general two-point functions and of generalized free fields in d-dimensional de Sitter space-time which closely parallels the corresponding minkowskian theory. The usual spectral condition is now replaced by a certain geodesic spectral condition, equivalent to a precise thermal characterization of the corresponding ``vacuum''states. Our method is based on the geometry of the complex de Sitter space-time and on the introduction of a class of holomorphic functions on this manifold, called perikernels, which reproduce mutatis mutandis the structural properties of the two-point correlation functions of the minkowskian quantum field theory. The theory contains as basic elementary case the linear massive field models in their ``preferred'' representation. The latter are described by the introduction of de Sitter plane waves in their tube domains which lead to a new integral representation of the two-point functions and to a Fourier-Laplace type transformation on the hyperboloid. The Hilbert space structure of these theories is then analysed by using this transformation. In particular we show the Reeh-Schlieder property. For general two-point functions, a substitute to the Wick rotation is defined both in complex space-time and in the complex mass variable, and substantial results concerning the derivation of Kallen-Lehmann type representation are obtained.},
2212         author = {J. Bros and U. Moschella},
2213         eprint = {gr-qc/9511019},
2214         journal = {Rev. Math. Phys.},
2215         localfile = {1996 - Bros, Moschella - Two-point Functions and Quantum Fields in de Sitter Universe.pdf},
2216         pages = {327--392},
2217         slaccitation = {\%\%CITATION = GR-QC/9511019\\;\%\%},
2218         title = {{Two-point Functions and Quantum Fields in de Sitter Universe}},
2219         url = {http://arxiv.org/abs/gr-qc/9511019},
2220         volume = {8},
2221         year = {1996}
2222 }
2223 
2224 @article{GrosseLechner:2007,
2225         abstract = {Within the setting of a recently proposed model of quantum fields on noncommutative Minkowski spacetime, the consequences of the consistent application of the proper, untwisted Poincare group as the symmetry group are investigated. The emergent model contains an infinite family of fields which are labelled by different noncommutativity parameters, and related to each other by Lorentz transformations. The relative localization properties of these fields are investigated, and it is shown that to each field one can assign a wedge-shaped localization region of Minkowski space. This assignment is consistent with the principles of covariance and locality, i.e. fields localized in spacelike separated wedges commute. Regarding the model as a non-local, but wedge-local, quantum field theory on ordinary (commutative) Minkowski spacetime, it is possible to determine two-particle S-matrix elements, which turn out to be non-trivial. Some partial negative results concerning the existence of observables with sharper localization properties are also obtained.},
2226         author = {H. Grosse and G. Lechner},
2227         doi = {10.1088/1126-6708},
2228         eprint = {arXiv:0706.3992 [hep-th]},
2229         journal = {JHEP},
2230         keywords = {kw:NC-Wick; kw:warping},
2231         localfile = {2007 - Grosse, Lechner - Wedge-Local Quantum Fields and Noncommutative Minkowski Space.pdf},
2232         pages = {012},
2233         slaccitation = {\%\%CITATION = ARXIV:0706.3992\\;\%\%},
2234         title = {{Wedge-Local Quantum Fields and Noncommutative {M}inkowski Space}},
2235         url = {http://arxiv.org/abs/0706.3992},
2236         volume = {11},
2237         x-color = {#199bff},
2238         year = {2007}
2239 }
2240 
2241 @article{Knight:1961,
2242         abstract = {A definition of strict localization of states in quantum field theory is presented. This definition is based on considering products of field operators as the primary measurable quantities of the theory. An example of a localized state is given, showing that such a state arises when a free field interacts with an external current that is limited to a bounded region of space-time. It is shown by means of a graphical technique that a state having a finite number of particles cannot satisfy the definition of localization. A simple representation of localized states is investigated, and arguments are given to support its generality and uniqueness. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.},
2243         author = {J. M. Knight},
2244         doi = {10.1063/1.1703731},
2245         journal = {J. Math. Phys.},
2246         localfile = {1961 - Knight - Strict Localization in Quantum Field Theory.pdf},
2247         number = {4},
2248         pages = {459--471},
2249         title = {{Strict Localization in Quantum Field Theory}},
2250         url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMAPAQ000002000004000459000001&idtype=cvips&gifs=yes},
2251         volume = {2},
2252         year = {1961}
2253 }
2254 
2255 @article{ChamseddineFelderFrhlich:1993,
2256         abstract = {The formalism of non-commutative geometry of A. Connes is used to construct models in particle physics. The physical space-time is taken to be a product of a continuous four-manifold by a discrete set of points. The treatment of Connes is modified in such a way that the basic algebra is defined over the space of matrices, and the breaking mechanism is planted in the Dirac operator. This mechanism is then applied to three examples. In the first example the discrete space consists of two points, and the two algebras are taken respectively to be those of $2\times 2$ and $1\times 1$ matrices. With the Dirac operator containing the vacuum breaking $SU(2)\times U(1)$ to $U(1)$, the model is shown to correspond to the standard model. In the second example the discrete space has three points, two of the algebras are identical and consist of $5\times 5$ complex matrices, and the third algebra consists of functions. With an appropriate Dirac operator this model is almost identical to the minimal $SU(5)$ model of Georgi and Glashow. The third and final example is the left-right symmetric model $SU(2)_L\times SU(2)_R\times U(1)_{B-L}.$},
2257         author = {A. H. Chamseddine and G. Felder and J. Fr{\"{o}}hlich},
2258         eprint = {hep-ph/9209224},
2259         journal = {Nucl. Phys.},
2260         localfile = {1993 - Chamseddine, Felder, Frohlich - Grand unification in noncommutative geometry.pdf},
2261         pages = {672--700},
2262         slaccitation = {\%\%CITATION = HEP-PH/9209224\\;\%\%},
2263         title = {{Grand unification in noncommutative geometry}},
2264         url = {http://arxiv.org/abs/hep-ph/9209224},
2265         volume = {B395},
2266         year = {1993}
2267 }
2268 
2269 @article{FrhlichFuchsRunkelSchweigert:2004,
2270         abstract = {Algebra and representation theory in modular tensor categories can be combined with tools from topological field theory to obtain a deeper understanding of rational conformal field theories in two dimensions: It allows us to establish the existence of sets of consistent correlation functions, to demonstrate some of their properties in a model-independent manner, and to derive explicit expressions for OPE coefficients and coefficients of partition functions in terms of invariants of links in three-manifolds. We show that a Morita class of (symmetric special) Frobenius algebras $A$ in a modular tensor category $\calc$ encodes all data needed to describe the correlators. A Morita-invariant formulation is provided by module categories over $\calc$. Together with a bimodule-valued fiber functor, the system (tensor category + module category) can be described by a weak Hopf algebra. The Picard group of the category $\calc$ can be used to construct examples of symmetric special Frobenius algebras. The Picard group of the category of $A$-bimodules describes the internal symmetries of the theory and allows one to identify generalized Kramers-Wannier dualities.},
2271         author = {J. Fr{\"{o}}hlich and J. Fuchs and I. Runkel and C. Schweigert},
2272         eprint = {math/0411507},
2273         localfile = {2004 - Fr\"{o}hlich, Fuchs, Runkel - Picard groups in rational conformal field theory.pdf},
2274         slaccitation = {\%\%CITATION = MATH/0411507\\;\%\%},
2275         title = {{Picard groups in rational conformal field theory}},
2276         url = {http://arxiv.org/abs/math/0411507},
2277         year = {2004}
2278 }
2279 
2280 @article{Mund:2003,
2281         abstract = {We discuss a concept of particle localization which is motivated from quantum field theory, and has been proposed by Brunetti, Guido and Longo and by Schroer. It endows the single particle Hilbert space with a family of real subspaces indexed by the space-time regions, with certain specific properties reflecting the principles of locality and covariance. We show by construction that such a localization structure exists also in the case of massive anyons in d=2+1, i.e. for particles with positive mass and with arbitrary spin s in the reals. The construction is completely intrinsic to the corresponding ray representation of the (proper orthochronous) Poincare group. Our result is of particular interest since there are no free fields for anyons, which would fix a localization structure in a straightforward way. We present explicit formulas for the real subspaces, expected to turn out useful for the construction of a quantum field theory for anyons. In accord with well-known results, only localization in string-like, instead of point-like or bounded, regions is achieved. We also prove a single-particle PCT theorem, exhibiting a PCT operator which acts geometrically correctly on the family of real subspaces.},
2282         author = {J. Mund},
2283         eprint = {hep-th/0208195},
2284         journal = {J. Math. Phys.},
2285         localfile = {2003 - Mund - Modular localization of massive particles with any spin in.pdf},
2286         pages = {2037--2057},
2287         slaccitation = {\%\%CITATION = HEP-TH/0208195\\;\%\%},
2288         title = {{Modular localization of massive particles with any spin in D = 2+1}},
2289         url = {http://arxiv.org/abs/hep-th/0208195},
2290         volume = {44},
2291         year = {2003}
2292 }
2293 
2294 @article{Mund:1998,
2295         abstract = {We show that a quantum field theoretic model of anyons cannot be ``free'' in the (restrictive) sense that the basic fields create only one-particle states out of the vacuum.},
2296         author = {J. Mund},
2297         eprint = {hep-th/9712119},
2298         journal = {Lett. Math. Phys.},
2299         localfile = {1997 - Mund - No-Go Theorem for Free Relativistic Anyons in d=2+1.pdf},
2300         pages = {319--328},
2301         slaccitation = {\%\%CITATION = HEP-TH/9712119\\;\%\%},
2302         title = {{No-go theorem for *free* relativistic anyons in d = 2+1}},
2303         url = {http://arxiv.org/abs/hep-th/9712119},
2304         volume = {43},
2305         year = {1998}
2306 }
2307 
2308 @article{Mund:2005,
2309         abstract = {We present a construction of string--localized covariant free quantum fields for a large class of irreducible (ray) representations of the Poincare group. Among these are the representations of mass zero and infinite spin, which are known to be incompatible with point-like localized fields. (Based on joint work with B.Schroer and J.Yngvason [13].)},
2310         author = {J. Mund},
2311         eprint = {hep-th/0502014},
2312         localfile = {2005 - Mund - String-localized covariant quantum fields.pdf},
2313         slaccitation = {\%\%CITATION = HEP-TH/0502014\\;\%\%},
2314         title = {{String-localized covariant quantum fields}},
2315         url = {http://arxiv.org/abs/hep-th/0502014},
2316         year = {2005}
2317 }
2318 
2319 @article{Wigner:1939,
2320         author = {E. P. Wigner},
2321         doi = {10.2307/1968551},
2322         journal = {Ann. Math.},
2323         localfile = {1939 - Wigner - On unitary representations of the inhomogeneous Lorentz group.pdf},
2324         title = {{On unitary representations of the inhomogeneous {L}orentz group}},
2325         volume = {40},
2326         year = {1939}
2327 }
2328 
2329 @article{BalachandranPinzulQureshi:2007,
2330         abstract = {It is by now well known that the Poincar\'{e} group acts on the Moyal plane with a twisted coproduct. Poincar\'{e} invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a twisted Poincar\'{e} action in quantum theories on the Moyal plane. We develop quantum field theories invariant under the twisted action from the representations of the Poincar\'{e} group, ensuring also the invariance of the S-matrix under the twisted action of the group . A significant new contribution here is the construction of the Poincar\'{e} generators using quantum fields.},
2331         author = {A. P. Balachandran and A. Pinzul and B. A. Qureshi},
2332         eprint = {arXiv:0708.1779 [hep-th]},
2333         keywords = {NCQFT},
2334         localfile = {2007 - Balachandran, Pinzul, Qureshi - Twisted Poincar'e Invariant Quantum Field Theories.pdf},
2335         slaccitation = {\%\%CITATION = ARXIV:0708.1779\\;\%\%},
2336         title = {{Twisted Poincar'e Invariant Quantum Field Theories}},
2337         url = {http://arxiv.org/abs/0708.1779},
2338         year = {2007}
2339 }
2340 
2341 @article{Steinacker:2007,
2342         abstract = {We show that the matrix-model action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4-dimensional case. The SU(n) gauge fields as well as additional scalar fields couple to an effective metric G\_{ab}, which is determined by a dynamical Poisson structure. The emergent gravity is intimately related to noncommutativity, encoding those degrees of freedom which are usually interpreted as U(1) gauge fields. This leads to a class of metrics which contains the physical degrees of freedom of gravitational waves, and allows to recover e.g. the Newtonian limit with arbitrary mass distribution. It also suggests a consistent picture of UV/IR mixing in terms of an induced gravity action. This should provide a suitable framework for quantizing gravity.},
2343         author = {H. Steinacker},
2344         journal = {JHEP},
2345         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
2346         pages = {049},
2347         pdf = {http://arxiv.org/pdf/0708.2426},
2348         title = {{Emergent Gravity from Noncommutative Gauge Theory}},
2349         url = {http://arxiv.org/abs/0708.2426},
2350         v1descr = {Mon, 20 Aug 2007 16:24:51 GMT (32kb)},
2351         v1url = {http://www.arxiv.org/abs/0708.2426v1},
2352         v2descr = {Tue, 13 Nov 2007 21:31:28 GMT (35kb)},
2353         v2url = {http://www.arxiv.org/abs/0708.2426v2},
2354         v3descr = {Wed, 19 Dec 2007 14:16:46 GMT (35kb)},
2355         volume = {0712},
2356         year = {2007}
2357 }
2358 
2359 @article{Hollands:2007,
2360         abstract = {We present a proof that quantum Yang-Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the non-commutative algebra of observables, in the sense of formal power series, as well as a space of corresponding quantum states. The algebra contains all gauge invariant, renormalized, interacting quantum field operators (polynomials in the field strength and its derivatives), and all their relations such as commutation relations or operator product expansion. It can be viewed as a deformation quantization of the Poisson algebra of classical Yang-Mills theory equipped with the Peierls bracket. The algebra is constructed as the cohomology of an auxiliary algebra describing a gauge fixed theory with ghosts and anti-fields. A key technical difficulty is to establish a suitable hierarchy of Ward identities at the renormalized level that ensure conservation of the interacting BRST-current, and that the interacting BRST-charge is nilpotent. The algebra of physical interacting field observables is obtained as the cohomology of this charge. As a consequence of our constructions, we can prove that the operator product expansion closes on the space of gauge invariant operators. Similarly, the renormalization group flow is proved not to leave the space of gauge invariant operators.},
2361         author = {S. Hollands},
2362         journal = {Rev. Math. Phys.},
2363         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
2364         pages = {1033--1172},
2365         pdf = {http://arxiv.org/pdf/0705.3340},
2366         title = {{Renormalized Quantum Yang-Mills Fields in Curved Spacetime}},
2367         url = {http://arxiv.org/abs/0705.3340},
2368         v1descr = {Wed, 23 May 2007 11:33:38 GMT (107kb)},
2369         v1url = {http://www.arxiv.org/abs/0705.3340v1},
2370         v2descr = {Wed, 13 Jun 2007 13:03:52 GMT (111kb)},
2371         v2url = {http://www.arxiv.org/abs/0705.3340v2},
2372         v3descr = {Thu, 28 Feb 2008 16:27:04 GMT (128kb)},
2373         volume = {20},
2374         year = {2008}
2375 }
2376 
2377 @article{Hollands:2007-1,
2378         abstract = {We present an algorithm for constructing the Wilson operator product expansion (OPE) for perturbative interacting quantum field theory in general Lorentzian curved spacetimes, to arbitrary orders in perturbation theory. The remainder in this expansion is shown to go to zero at short distances in the sense of expectation values in arbitrary Hadamard states. We also establish a number of general properties of the OPE coefficients: (a) they only depend (locally and covariantly) upon the spacetime metric and coupling constants, (b) they satisfy an associativity property, (c) they satisfy a renormalization group equation, (d) they satisfy a certain microlocal wave front set condition, (e) they possess a ``scaling expansion''. The latter means that each OPE coefficient can be written as a sum of terms, each of which is the product of a curvature polynomial at a spacetime point, times a Lorentz invariant Minkowski distribution in the tangent space of that point. The algorithm is illustrated in an example.},
2379         author = {S. Hollands},
2380         eprint = {gr-qc/0605072},
2381         journal = {Commun. Math. Phys.},
2382         localfile = {2007 - Hollands - The operator product expansion for perturbative quantum field theory in curved spacetime.pdf},
2383         pages = {1--36},
2384         slaccitation = {\%\%CITATION = GR-QC/0605072\\;\%\%},
2385         title = {{The operator product expansion for perturbative quantum field theory in curved spacetime}},
2386         url = {http://arxiv.org/abs/gr-qc/0605072},
2387         volume = {273},
2388         year = {2007}
2389 }
2390 
2391 @article{Hollands:2004,
2392         abstract = {We consider the operator product expansion for quantum field theories on general analytic 4-dimensional curved spacetimes within an axiomatic framework. We prove under certain general, model-independent assumptions that such an expansion necessarily has to be invariant under a simultaneous reversal of parity, time, and charge (PCT) in the following sense: The coefficients in the expansion of a product of fields on a curved spacetime with a given choice of time and space orientation are equal (modulo complex conjugation) to the coefficients for the product of the corresponding charge conjugate fields on the spacetime with the opposite time and space orientation. We propose that this result should be viewed as a replacement of the usual PCT theorem in Minkowski spacetime, at least in as far as the algebraic structure of the quantum fields at short distances is concerned.},
2393         author = {S. Hollands},
2394         eprint = {gr-qc/0212028},
2395         journal = {Commun. Math. Phys.},
2396         localfile = {2004 - Hollands - A general PCT theorem for the operator product expansion in curved spacetime.pdf},
2397         pages = {209--244},
2398         slaccitation = {\%\%CITATION = GR-QC/0212028\\;\%\%},
2399         title = {{A general PCT theorem for the operator product expansion in curved spacetime}},
2400         url = {http://arxiv.org/abs/gr-qc/0212028},
2401         volume = {244},
2402         year = {2004}
2403 }
2404 
2405 @article{KeylMatsuiSchlingemannWerner:2007,
2406         abstract = {We consider quantum spin chains and their translationally invariant pure states. We prove Haag duality for quasilocal observables localized in semi-infinite intervals when the von Neumann algebras generated by observables localized in these intervals are not type I.},
2407         author = {M. Keyl and T. Matsui and D. Schlingemann and R. F. Werner},
2408         journal = {Rev. Math. Phys.},
2409         keywords = {Mathematical Physics (math-ph)},
2410         pages = {707--724},
2411         pdf = {http://arxiv.org/pdf/math-ph/0703013},
2412         title = {{On Haag Duality for Pure States of Quantum Spin Chain}},
2413         url = {http://arxiv.org/abs/math-ph/0703013},
2414         v1descr = {Fri, 2 Mar 2007 06:32:05 GMT (17kb)},
2415         volume = {20},
2416         year = {2008}
2417 }
2418 
2419 @article{GerardJkel:2006,
2420         author = {C. Gerard and C. D. J{\"{a}}kel},
2421         eprint = {math-ph/0609088},
2422         localfile = {2006 - Gerard, J\"{a}kel - On the relativistic KMS condition for the P(phi)(2) model.pdf},
2423         slaccitation = {\%\%CITATION = MATH-PH/0609088\\;\%\%},
2424         title = {{On the relativistic KMS condition for the P(phi)(2) model}},
2425         year = {2006}
2426 }
2427 
2428 @article{GerardJkel:2005,
2429         abstract = {The relativistic KMS condition introduced by Bros and Buchholz provides a link between quantum statistical mechanics and quantum field theory. We show that for the $P(\phi)_2$ model at positive temperature, the two point function for fields satisfies the relativistic KMS condition.},
2430         author = {C. Gerard and C. D. J{\"{a}}kel},
2431         eprint = {math-ph/0403048},
2432         journal = {Rev. Math. Phys.},
2433         localfile = {2005 - Gerard, J\"{a}kel - Thermal quantum fields without cut-offs in 1+1 space-time dimensions.pdf},
2434         pages = {113--174},
2435         slaccitation = {\%\%CITATION = MATH-PH/0403048\\;\%\%},
2436         title = {{Thermal quantum fields without cut-offs in 1+1 space-time dimensions}},
2437         url = {http://arxiv.org/abs/math-ph/0609088},
2438         volume = {17},
2439         year = {2005}
2440 }
2441 
2442 @article{GerardJkel:2003,
2443         abstract = {We construct interacting quantum fields in 1+1 space-time dimensions, representing charged or neutral scalar bosons at positive temperature and zero chemical potential. Our work is based on prior work by Klein and Landau and Hoegh-Krohn. Generalized path space methods are used to add a spatially cut-off interaction to the free system, which is described in the Araki-Woods representation. It is shown that the interacting KMS state is normal w.r.t. the Araki-Woods representation. The observable algebra and the modular conjugation of the interacting system are shown to be identical to the ones of the free system and the interacting Liouvillean is described in terms of the free Liouvillean and the interaction.},
2444         author = {C. Gerard and C. D. J{\"{a}}kel},
2445         eprint = {math-ph/0307053},
2446         localfile = {2003 - Gerard, J\"{a}kel - Thermal quantum fields with spatially cut-off interactions in 1+1 space-time dimensions.pdf},
2447         slaccitation = {\%\%CITATION = MATH-PH/0307053\\;\%\%},
2448         title = {{Thermal quantum fields with spatially cut-off interactions in 1+1 space-time dimensions}},
2449         url = {http://arxiv.org/abs/math-ph/0307053},
2450         year = {2003}
2451 }
2452 
2453 @article{JaffeJkel:2006,
2454         abstract = {We establish a useful identity for intertwining a creation or annihilation operator with the heat kernel of a self-interacting bosonic field theory.},
2455         author = {A. Jaffe and C. D. J{\"{a}}kel},
2456         eprint = {math-ph/0507047},
2457         journal = {Commun. Math. Phys.},
2458         localfile = {2006 - Jaffe, J\"{a}kel - An exchange identity for non-linear fields.pdf},
2459         pages = {283--289},
2460         slaccitation = {\%\%CITATION = MATH-PH/0507047\\;\%\%},
2461         title = {{An exchange identity for non-linear fields}},
2462         url = {http://arxiv.org/abs/math-ph/0507047},
2463         volume = {264},
2464         year = {2006}
2465 }
2466 
2467 @article{Abe:2007-1,
2468         abstract = {The space-time symmetry of noncommutative quantum field theories with a deformed quantization is described by the twisted Poincar\'{e} algebra, while that of standard commutative quantum field theories is described by the Poincar\'{e} algebra. Based on the equivalence of the deformed theory with a commutative field theory, the correspondence between the twisted Poincar\'{e} symmetry of the deformed theory and the Poincar\'{e} symmetry of a commutative theory is established. As a by-product, we obtain the conserved charge associated with the twisted Poincar\'{e} transformation to make the twisted Poincar\'{e} symmetry evident in the deformed theory. Our result implies that the equivalence between the commutative theory and the deformed theory holds in a deeper level, i.e., it holds not only in correlation functions but also in (different types of) symmetries.},
2469         author = {Y. Abe},
2470         journal = {Phys. Rev. D},
2471         keywords = {High Energy Physics - Theory (hep-th)},
2472         number = {KEK-TH-1177},
2473         pages = {125009},
2474         pdf = {http://arxiv.org/pdf/0709.1010},
2475         title = {{On the Correspondence between Poincar\'{e} Symmetry of Commutative QFT and Twisted Poincar\'{e} Symmetry of Noncommutative QFT}},
2476         url = {http://arxiv.org/abs/0709.1010},
2477         v1descr = {Fri, 7 Sep 2007 07:38:53 GMT (13kb)},
2478         v1url = {http://www.arxiv.org/abs/0709.1010v1},
2479         v2descr = {Fri, 16 May 2008 06:57:30 GMT (14kb)},
2480         volume = {77},
2481         year = {2008}
2482 }
2483 
2484 @article{ZamolodchikovZamolodchikov:1979,
2485         abstract = {The general properties of the factorized S-matrix in two-dimensional space-time are considered. The relation between the factorization property of the scattering theory and the infinite number of conservation laws of the underlying field theory is discussed. The factorization of the total S-matrix is shown to impose hard restrictions on two-particle matrix elements: they should satisfy special identities, the so-called factorization equations. The general solution of the unitarity, crossing and factorization equations is found for the S-matrices having isotopic O(N)-symmetry. The solution turns out to have different properties for the cases N = 2 and N greater-or-equal, slanted 3. For N = 2 the general solution depends on one parameter (of coupling constant type), whereas the solution for N greater-or-equal, slanted 3 has no parameters but depends analytically on N. The solution for N = 2 is shown to be an exact soliton S-matrix of the sine-Gordon model (equivalently the massive Thirring model). The total S-matrix of the model is constructed. In the case of N greater-or-equal, slanted 3 there are two ``minimum'' solutions, i.e., those having a minimum set of singularities. One of them is shown to be an exact S matrix of the quantum O(N)-symmetric nonlinear σ-model, the other is argued to describe the scattering of elementary particles of the Gross-Neveu model.},
2486         author = {A. B. Zamolodchikov and A. B. Zamolodchikov},
2487         doi = {10.1016/0003-4916(79)90391-9},
2488         journal = {Annals Phys.},
2489         localfile = {1979 - Zamolodchikov, Zamolodchikov - Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models.pdf},
2490         pages = {253--291},
2491         slaccitation = {\%\%CITATION = APNYA,120,253\\;\%\%},
2492         title = {{Factorized {S}-matrices in two dimensions as the exact solutions of certain relativistic quantum field models}},
2493         volume = {120},
2494         year = {1979}
2495 }
2496 
2497 @book{GlimmJaffe:1987,
2498         address = {New York},
2499         author = {J. Glimm and A. Jaffe},
2500         edition = {2},
2501         keywords = {kw:NC-Wick},
2502         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Glimm, Jaffe - Quantum Physics - A Functional Integral Point of View.djvu},
2503         note = {New York, Usa: Springer ( 1987) 535p},
2504         publisher = {Springer},
2505         title = {{Quantum Physics. A Functional Integral Point Of View}},
2506         year = {1987}
2507 }
2508 
2509 @article{Borchers:1992,
2510         abstract = {Let Jί be a von Neumann algebra with cyclic and separating vector Ω, and let U(a) be a continuous unitary representation of R with positive generator and Ω as fixed point. If these unitaries induce for positive arguments endo- morphisms of Jί then the modular group act as dilatations on the group of unitaries. Using this it will be shown that every theory of local observables in two dimensions, which is covariant under translations only, can be imbedded into a theory of local observables covariant under the whole Poincare group. This theory is also covariant under the CPT-transformation.},
2511         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
2512         doi = {10.1007/BF02099011},
2513         journal = {Commun. Math. Phys.},
2514         localfile = {1992 - Borchers - The CPT-theorem in two-dimensional theories of local observables.pdf},
2515         pages = {315--332},
2516         slaccitation = {\%\%CITATION = CMPHA,143,315\\;\%\%},
2517         title = {{The CPT theorem in two-dimensional theories of local observables}},
2518         volume = {143},
2519         year = {1992}
2520 }
2521 
2522 @article{KahlerWiesbrock:2001,
2523         author = {R. Kahler and H.W. Wiesbrock},
2524         journal = {J. Math. Phys.},
2525         pages = {74--86},
2526         slaccitation = {\%\%CITATION = JMAPA,42,74\\;\%\%},
2527         title = {{Modular theory and the reconstruction of four-dimensional quantum field theories}},
2528         volume = {42},
2529         year = {2001}
2530 }
2531 
2532 @article{SchroerWiesbrock:2000,
2533         author = {B. Schroer and H.W. Wiesbrock},
2534         eprint = {hep-th/9901031},
2535         journal = {Rev. Math. Phys.},
2536         pages = {461--473},
2537         slaccitation = {\%\%CITATION = HEP-TH/9901031\\;\%\%},
2538         title = {{Looking beyond the thermal horizon: Hidden symmetries in chiral models}},
2539         volume = {12},
2540         year = {2000}
2541 }
2542 
2543 @article{SchroerWiesbrock:2000-2,
2544         abstract = {In this letter we present some new results on modular theory and its application in quantum field theory. In doing this we develop some new proposals how to generalize concepts of geometrical action. Therefore the spirit of this letter is more on a programmatic side with many details remaining to be elaborated.},
2545         author = {B. Schroer and H.W. Wiesbrock},
2546         eprint = {math-ph/9809003},
2547         journal = {Rev. Math. Phys.},
2548         localfile = {1998 - Schroer, Wiesbrock - Modular Theory and Geometry.pdf},
2549         pages = {139--158},
2550         slaccitation = {\%\%CITATION = MATH-PH/9809003\\;\%\%},
2551         title = {{Modular theory and geometry}},
2552         url = {http://arxiv.org/abs/math-ph/9809003},
2553         volume = {12},
2554         year = {2000}
2555 }
2556 
2557 @article{Wiesbrock:1997,
2558         abstract = {Let $\mathcal{N},\mathcal{M} $ be von Neumann algebras acting on a Hilbert space $\mathcal{H} $ and let ${\O}mega \in \mathcal{H} $ be a common cyclic and separating vector. We say that $(\mathcal{N},\mathcal{M},{\O}mega ) $ have the {\em modular intersection property} with respect to ${\O}mega $ if \vspace{6pt} \begin{itemize} \item [(1)] $((\mathcal{N} \cap \mathcal{M}) \subset \mathcal{N},{\O}mega ),((\mathcal{N} \cap \mathcal{M}) \subset \mathcal{M},{\O}mega ) $ -half-sided modular inclusions, \item [(2)] $J\_\mathcal{N} (s - {\l}im \_{t \to \infty } \Delta \_\mathcal{N}^{it} \Delta \_\mathcal{M}^{ - it} )J\_\mathcal{N} = s - {\l}im \_{t \to \infty } \Delta \_\mathcal{M}^{it} \Delta \_\mathcal{N}^{ - it} . $ \end{itemize} \vspace{6pt} (If (1) holds the strong limit exists.) We show that under these conditions the modular groups of $\mathcal{N} $ and $\mathcal{M} $ generate a 2-dim. Lie group. This observation is the basis for obtaining group representations of Sl(2,\, $\mathbb{R} $ )/Z 2 generated by modular groups. operator algebras - quantum field theory - von Neumann algebras.},
2559         author = {H.W. Wiesbrock},
2560         journal = {Lett. Math. Phys.},
2561         localfile = {1997 - Wiesbrock - Symmetries and Modular Intersections of Von Neumann Algebras.pdf},
2562         pages = {203--212},
2563         slaccitation = {\%\%CITATION = LMPHD,39,203\\;\%\%},
2564         title = {{Symmetries and modular intersections of von Neumann algebras}},
2565         volume = {39},
2566         year = {1997}
2567 }
2568 
2569 @article{Wiesbrock:1998,
2570         abstract = {We show that modular intersections of von Neumann algebras occur naturally in quantum field theory. An example are local observable algebras associated with wedge regions, which have a lightray in common, see also [Bo 2, Wi 3]. Conversely, starting from a set of four algebras lying in a specified modular position relative to each other we construct a net of local observables of a 2+1 dimensional quantum field theory.},
2571         author = {H.W. Wiesbrock},
2572         journal = {Commun. Math. Phys.},
2573         localfile = {1998 - Wiesbrock - Modular Intersections of von Neumann Algebras in Quantum Field Theory.pdf},
2574         pages = {269--285},
2575         slaccitation = {\%\%CITATION = CMPHA,193,269\\;\%\%},
2576         title = {{Modular intersections of von-Neumann-algebras in quantum field theory}},
2577         volume = {193},
2578         year = {1998}
2579 }
2580 
2581 @article{NillWiesbrock:1995,
2582         author = {Florian Nill and H.W. Wiesbrock},
2583         eprint = {hep-th/9411084},
2584         journal = {Rev. Math. Phys.},
2585         pages = {599--630},
2586         slaccitation = {\%\%CITATION = HEP-TH/9411084\\;\%\%},
2587         title = {{A Comment on Jones inclusions with infinite index}},
2588         volume = {7},
2589         year = {1995}
2590 }
2591 
2592 @article{Wiesbrock:1995,
2593         author = {H.W. Wiesbrock},
2594         journal = {Rev. Math. Phys.},
2595         pages = {133--160},
2596         slaccitation = {\%\%CITATION = RMPHE,7,133\\;\%\%},
2597         title = {{Superselection structure of conformal field theory on the circle and localized Connes' cocycles}},
2598         volume = {7},
2599         year = {1995}
2600 }
2601 
2602 @article{Wiesbrock:1994,
2603         author = {H.W. Wiesbrock},
2604         journal = {Lett. Math. Phys.},
2605         localfile = {1994 - Wiesbrock - A note on strongly additive conformal field theory and half-sided modular conormal standard inclusions.pdf},
2606         pages = {303--308},
2607         slaccitation = {\%\%CITATION = LMPHD,31,303\\;\%\%},
2608         title = {{A Note on strongly additive conformal field theory and half sided modular conormal standard inclusions}},
2609         volume = {31},
2610         year = {1994}
2611 }
2612 
2613 @article{Wiesbrock:1993,
2614         author = {H.W. Wiesbrock},
2615         journal = {Commun. Math. Phys.},
2616         localfile = {1993 - Wiesbrock - Conformal quantum field theory and half-sided modular inclusions of von Neumann algebras.pdf},
2617         pages = {537--544},
2618         slaccitation = {\%\%CITATION = CMPHA,158,537\\;\%\%},
2619         title = {{Conformal quantum field theory and half sided modular inclusions of von Neumann algebras}},
2620         volume = {158},
2621         year = {1993}
2622 }
2623 
2624 @article{Wiesbrock:1992-1,
2625         author = {H.W. Wiesbrock},
2626         journal = {J. Math. Phys.},
2627         pages = {1837--1840},
2628         slaccitation = {\%\%CITATION = JMAPA,33,1837\\;\%\%},
2629         title = {{A Note on the construction of the C* algebra of bosonic strings}},
2630         volume = {33},
2631         year = {1992}
2632 }
2633 
2634 @article{Wiesbrock:1992,
2635         author = {H.W. Wiesbrock},
2636         journal = {Commun. Math. Phys.},
2637         pages = {17--42},
2638         slaccitation = {\%\%CITATION = CMPHA,145,17\\;\%\%},
2639         title = {{The Construction of the sh Lie algebra of closed bosonic strings}},
2640         volume = {145},
2641         year = {1992}
2642 }
2643 
2644 @article{Wiesbrock:1993-1,
2645         abstract = {Abstract. Let Jf a M be von-Neumann-Algebras on a Hubert space Jf, Ω a com- mon cyclic and separating vector. Denote ΔM, Δjf resp. JMy J^ the associated modular operators and conjugations. Assume Δ^ιtJfΔ^ιt a Jf for t ^ 0. We call such an inclusion half-sided modular. Then we prove the existence of a one- parameter unitary group U(a) on Jf, a e R, with generator ... and relations 1. ..., 2. ..., 3. ... 4. .... If Ji is a factor and Ώ is also cyclic for Jf' n , we show that ... has to be of type III,.},
2646         author = {H.W. Wiesbrock},
2647         journal = {Commun. Math. Phys.},
2648         localfile = {1993 - Wiesbrock - Half-sided modular inclusions of von-Neumann-algebras.pdf},
2649         pages = {83--92},
2650         slaccitation = {\%\%CITATION = CMPHA,157,83\\;\%\%},
2651         title = {{Half sided modular inclusions of von Neumann algebras}},
2652         volume = {157},
2653         year = {1993}
2654 }
2655 
2656 @article{Wiesbrock:1992-2,
2657         author = {H.W. Wiesbrock},
2658         journal = {Lett. Math. Phys.},
2659         localfile = {1992 - Wiesbrock - A comment on a recent work of Borchers.pdf},
2660         pages = {157--160},
2661         slaccitation = {\%\%CITATION = LMPHD,25,157\\;\%\%},
2662         title = {{A Comment on a recent work of Borchers}},
2663         volume = {25},
2664         year = {1992}
2665 }
2666 
2667 @article{Wiesbrock:1991,
2668         author = {H.W. Wiesbrock},
2669         journal = {Commun. Math. Phys.},
2670         pages = {369--397},
2671         slaccitation = {\%\%CITATION = CMPHA,136,369\\;\%\%},
2672         title = {{The C* algebra of bosonic strings}},
2673         volume = {136},
2674         year = {1991}
2675 }
2676 
2677 @article{BorchersBuchholzSchroer:2001,
2678         abstract = {Polarization-free generators, i.e. ``interacting'' Heisenberg operators which are localized in wedge-shaped regions of Minkowski space and generate single particle states from the vacuum, are a novel tool in the analysis and synthesis of two-dimensional integrable quantum field theories. In the present article, the status of these generators is analyzed in a general setting. It is shown that such operators exist in any theory and in any number of spacetime dimensions. But in more than two dimensions they have rather delicate domain properties in the presence of interaction. If, for example, they are defined and temperate on a translation-invariant, dense domain, then the underlying theory yields only trivial scattering. In two-dimensional theories, these domain properties are consistent with non-trivial interaction, but they exclude particle production. Thus the range of applications of polarization-free generators seems to be limited to the realm of two-dimensional theories.},
2679         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and D. Buchholz and B. Schroer},
2680         doi = {10.1007/s002200100411},
2681         eprint = {hep-th/0003243},
2682         journal = {Commun. Math. Phys.},
2683         localfile = {2000 - Borchers, Buchholz, Schroer - Polarization-free generators and the S-matrix.pdf},
2684         pages = {125--140},
2685         slaccitation = {\%\%CITATION = HEP-TH/0003243\\;\%\%},
2686         title = {{Polarization-free generators and the {S}-matrix}},
2687         url = {http://arxiv.org/abs/hep-th/0003243},
2688         volume = {219},
2689         year = {2001}
2690 }
2691 
2692 @article{Yngvason:1970,
2693         abstract = {It is shown that a local quantized field with a manifestly covariant transformation law under the Poincare group cannot have nonvanishing matrix elements between the vacuum and an irreducible subspace of zero mass and infinite spin.},
2694         author = {J. Yngvason},
2695         journal = {Commun. Math. Phys.},
2696         localfile = {1970 - Yngvason - Zero-mass infinite spin representations of the Poincare group and quantum field theory.pdf},
2697         pages = {195--203},
2698         slaccitation = {\%\%CITATION = CMPHA,18,195\\;\%\%},
2699         title = {{Zero-mass infinite spin representations of the poincare group and quantum field theory}},
2700         url = {http://projecteuclid.org/euclid.cmp/1103842535},
2701         volume = {18},
2702         year = {1970}
2703 }
2704 
2705 @article{BuchholzDAntoniLongo:1990,
2706         author = {D. Buchholz and C. D'Antoni and R. Longo},
2707         journal = {Commun. Math. Phys.},
2708         localfile = {1990 - Buchholz, D'Antoni, Longo - Nuclear maps and modular structures. II. Applications to quantum field theory.pdf},
2709         pages = {115},
2710         slaccitation = {\%\%CITATION = CMPHA,129,115\\;\%\%},
2711         title = {{Nuclear Maps and Modular Structures 2: Applications to Quantum Field Theory}},
2712         volume = {129},
2713         year = {1990}
2714 }
2715 
2716 @article{BuchholzDAntoniLongo:1990-1,
2717         author = {D. Buchholz and C. D'Antoni and R. Longo},
2718         journal = {J. Funct. Anal.},
2719         localfile = {1990 - Buchholz, D'Antoni, Longo - Nuclear maps and modular structures 1 - general properties.pdf},
2720         pages = {233--250},
2721         title = {{Nuclear maps and modular structures. I. General properties.}},
2722         volume = {88},
2723         year = {1990}
2724 }
2725 
2726 @article{Fewster:2005,
2727         author = {C. J. Fewster},
2728         eprint = {math-ph/0502002},
2729         slaccitation = {\%\%CITATION = MATH-PH/0502002\\;\%\%},
2730         title = {{Quantum energy inequalities and stability conditions in quantum field theory}},
2731         year = {2005}
2732 }
2733 
2734 @article{BuchholzSummers:2004-1,
2735         author = {D. Buchholz and S. J. Summers},
2736         eprint = {math-ph/0309023},
2737         journal = {Commun. Math. Phys.},
2738         pages = {625--641},
2739         slaccitation = {\%\%CITATION = MATH-PH/0309023\\;\%\%},
2740         title = {{An algebraic characterization of vacuum states in Minkowski space. III: Poincare covariance}},
2741         volume = {246},
2742         year = {2004}
2743 }
2744 
2745 @article{BuchholzSummers:2004-2,
2746         author = {D. Buchholz and S. J. Summers},
2747         doi = {10.1063/1.1804230},
2748         eprint = {math-ph/0407011},
2749         journal = {J. Math. Phys.},
2750         localfile = {2004 - Buchholz, Summers - Stable quantum systems in anti-de Sitter space: Causality, independence and spectral properties.pdf},
2751         pages = {4810--4831},
2752         slaccitation = {\%\%CITATION = MATH-PH/0407011\\;\%\%},
2753         title = {{Stable quantum systems in anti-de Sitter space: Causality, independence and spectral properties}},
2754         url = {http://www.arxiv.org/abs/math-ph/0407011},
2755         volume = {45},
2756         year = {2004}
2757 }
2758 
2759 @inproceedings{Rivasseau:2007,
2760         abstract = {A new version of scale analysis and renormalization theory has been found on the non-commutative Moyal space. It could be useful for physics beyond the standard model or for standard physics in strong external field. The good news is that quantum field theory is better behaved on non-commutative than on ordinary space: indeed it has no Landau ghost. Noncommutativity might therefore be an alternative to supersymmetry. We review this rapidly growing subject.},
2761         author = {V. Rivasseau},
2762         booktitle = {{S\'{e}minaire Poincar\'{e} X}},
2763         eprint = {arXiv:0705.0705 [hep-th]},
2764         localfile = {2007 - Rivasseau - Non-commutative renormalization.pdf},
2765         location = {Paris},
2766         pages = {15--95},
2767         slaccitation = {\%\%CITATION = ARXIV:0705.0705\\;\%\%},
2768         title = {{Non-commutative renormalization}},
2769         url = {http://arxiv.org/abs/0705.0705},
2770         year = {2007}
2771 }
2772 
2773 @article{Aks:1965,
2774         author = {S. {\AA}ks},
2775         doi = {10.1063/1.1704305},
2776         journal = {J. Math. Phys.},
2777         localfile = {1965 - Aks - Proof that Scattering Implies Production in Quantum Field Theory.pdf},
2778         pages = {516--532},
2779         title = {{Proof that scattering implies production in quantum field theory}},
2780         volume = {6},
2781         year = {1965}
2782 }
2783 
2784 @book{Araki:1999,
2785         address = {Oxford},
2786         author = {H. Araki},
2787         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Araki - Mathematical Theory of Quantum Fields.djvu},
2788         publisher = {Oxford University Press},
2789         series = {{Int. Series of Monographs on Physics}},
2790         title = {{Mathematical Theory of Quantum Fields}},
2791         year = {1999}
2792 }
2793 
2794 @article{ChaichianKulishNishijimaTureanu:2004,
2795         abstract = {By invoking the concept of twisted Poincar\' e symmetry of the algebra of functions on a Minkowski space-time, we demonstrate that the noncommutative space-time with the commutation relations $[x_\mu,x_\nu]=i\theta_{\mu\nu}$, where $\theta_{\mu\nu}$ is a {\it constant} real antisymmetric matrix, can be interpreted in a Lorentz-invariant way. The implications of the twisted Poincar\'{e} symmetry on QFT on such a space-time is briefly discussed. The presence of the twisted symmetry gives justification to all the previous treatments within NC QFT using Lorentz invariant quantities and the representations of the usual Poincar\'{e} symmetry.},
2796         author = {M. Chaichian and P. P. Kulish and K. Nishijima and A. Tureanu},
2797         eprint = {hep-th/0408069},
2798         journal = {Phys. Lett.},
2799         keywords = {NCQFT},
2800         localfile = {2004 - Chaichian, Kulish, Nishijima - On a Lorentz-invariant interpretation of noncommutative space-time and its implications on noncommutative QFT.pdf},
2801         pages = {98--102},
2802         slaccitation = {\%\%CITATION = HEP-TH/0408069\\;\%\%},
2803         title = {{On a {L}orentz-invariant interpretation of noncommutative space-time and its implications on noncommutative {QFT}}},
2804         url = {http://arxiv.org/abs/hep-th/0408069},
2805         volume = {B604},
2806         year = {2004}
2807 }
2808 
2809 @article{DouglasNekrasov:2001,
2810         abstract = {We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory, and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, both on the classical and quantum level. To appear in Reviews of Modern Physics.},
2811         author = {M. R. Douglas and N. A. Nekrasov},
2812         eprint = {hep-th/0106048},
2813         journal = {Rev. Mod. Phys.},
2814         localfile = {2001 - Douglas, Nekrasov - Noncommutative field theory.pdf},
2815         pages = {977--1029},
2816         slaccitation = {\%\%CITATION = HEP-TH/0106048\\;\%\%},
2817         title = {{Noncommutative field theory}},
2818         url = {http://arxiv.org/abs/hep-th/0106048},
2819         volume = {73},
2820         year = {2001}
2821 }
2822 
2823 @article{BuchholzSummers:2007,
2824         abstract = {We study a weakly local, but nonlocal model in spacetime dimension d>=2 and prove that it is maximally nonlocal in a certain specific quantitative sense. Nevertheless, depending on the number of dimensions d, it has string-localized or brane-localized operators which commute at spatial distances. In two spacetime dimensions, the model even comprises a covariant and local subnet of operators localized in bounded subsets of Minkowski space which has a nontrivial scattering matrix. The model thus exemplifies the algebraic construction of local operators from algebras associated with nonlocal fields.},
2825         author = {D. Buchholz and S. J. Summers},
2826         doi = {10.1088/1751-8113},
2827         eprint = {math-ph/0512060},
2828         journal = {J. Phys.},
2829         localfile = {2007 - Buchholz, Summers - String- and Brane-Localized Causal Fields in a Strongly Nonlocal Model.pdf},
2830         pages = {2147--2163},
2831         slaccitation = {\%\%CITATION = MATH-PH/0512060\\;\%\%},
2832         title = {{String- and brane-localized fields in a strongly nonlocal model}},
2833         url = {http://arxiv.org/abs/math-ph/0512060},
2834         volume = {A40},
2835         year = {2007}
2836 }
2837 
2838 @inbook{Faddeev:1984,
2839         author = {L. D. Faddeev},
2840         editor = {S. P. Novikov},
2841         note = {In Novikov, S.p. ( Ed.): Mathematical Physics Reviews, Vol. 1, 107-155},
2842         pages = {107--155},
2843         series = {{Mathematical Physics Reviews}},
2844         title = {{Quantum completely integrable models in field theory}},
2845         volume = {1},
2846         year = {1984}
2847 }
2848 
2849 @article{Grosse:1979,
2850         abstract = {Quantizing the operators of a Lax pair gives the in-field in terms of the interacting field. With the help of the Merchenko equation we obtain the inverse mapping for the quantized theory.},
2851         author = {H. Grosse},
2852         journal = {Phys. Lett. B},
2853         localfile = {1979 - Grosse - On the construction of m\"{o}ller operators for the nonlinear schr\"{o}dinger equation.pdf},
2854         pages = {267--271},
2855         title = {{On the Construction of {M}\"{o}ller Operators for the Nonlinear {S}chr\"{o}dinger Equation}},
2856         volume = {86},
2857         year = {1979}
2858 }
2859 
2860 @book{Iagolnitzer:1993,
2861         address = {Princeton},
2862         author = {D. Iagolnitzer},
2863         publisher = {Princeton University Press},
2864         title = {{Scattering in Quantum Field Theories}},
2865         year = {1993}
2866 }
2867 
2868 @article{Hepp:1965,
2869         author = {K. Hepp},
2870         booktitle = {{Brandeis University Summer Institute in Theoretical Physics: Axiomatic Field Theory}},
2871         doi = {10.1007/BF01646494},
2872         editor = {M. Chretien and S. Deser},
2873         journal = {Commun. Math. Phys.},
2874         localfile = {1965 - Hepp - On the connection between the LSZ and Wightman quantum field theory.pdf},
2875         pages = {95--111},
2876         publisher = {Gordon \& Breach},
2877         title = {{On the connection between {W}ightman and {LSZ} quantum field theory}},
2878         volume = {1},
2879         year = {1965}
2880 }
2881 
2882 @article{KuckertLorenzen:2007,
2883         abstract = {The analysis of the relation between modular P$_1$CT-symmetry -- a consequence of the Unruh effect -- and Pauli's spin-statistics relation is continued. The result in the predecessor to this article is extended to the Lorentz symmetric situation. A model $\G_L$ of the universal covering $\widetilde{L_+^\uparrow}\cong SL(2,\complex)$ of the restricted Lorentz group $L_+^\uparrow$ is modelled as a reflection group at the classical level. Based on this picture, a representation of $\G_L$ is constructed from pairs of modular P$_1$CT-conjugations, and this representation can easily be verified to satisfy the spin-statistics relation.},
2884         author = {B. Kuckert and R. Lorenzen},
2885         eprint = {math-ph/0512068},
2886         journal = {Commun. Math. Phys.},
2887         localfile = {2007 - Kuckert, Lorenzen - Spin, statistics, and reflections. II: Lorentz invariance.pdf},
2888         pages = {809--831},
2889         slaccitation = {\%\%CITATION = MATH-PH/0512068\\;\%\%},
2890         title = {{Spin, statistics, and reflections. {II}: {L}orentz invariance}},
2891         url = {http://arxiv.org/abs/math-ph/0512068},
2892         volume = {269},
2893         year = {2007}
2894 }
2895 
2896 @article{Lechner:2003,
2897         abstract = {A new approach to the inverse scattering problem proposed by Schroer, is applied to two-dimensional integrable quantum field theories. For any two-particle S-matrix S\_2 which is analytic in the physical sheet, quantum fields are constructed which are localizable in wedge-shaped regions of Minkowski space and whose two-particle scattering is described by the given \S\_2. These fields are polarization-free in the sense that they create one-particle states from the vacuum without polarization clouds. Thus they provide examples of temperate polarization-free generators in the presence of non-trivial interaction.},
2898         author = {G. Lechner},
2899         doi = {10.1023/A:1025772304804},
2900         eprint = {hep-th/0303062},
2901         journal = {Lett. Math. Phys.},
2902         localfile = {2003 - Lechner - Polarization-Free Quantum Fields and Interaction.pdf},
2903         pages = {137--154},
2904         slaccitation = {\%\%CITATION = HEP-TH/0303062\\;\%\%},
2905         title = {{Polarization-free quantum fields and interaction}},
2906         url = {http://arxiv.org/abs/hep-th/0303062},
2907         volume = {64},
2908         x-color = {#199bff},
2909         year = {2003}
2910 }
2911 
2912 @article{Lechner:2008,
2913         abstract = {A new approach to the construction of interacting quantum field theories on two-dimensional Minkowski space is discussed. In this program, models are obtained from a prescribed factorizing S-matrix in two steps. At first, quantum fields which are localized in infinitely extended, wedge-shaped regions of Minkowski space are constructed explicitly. In the second step, local observ ables are analyzed with operator-algebraic techniques, in particular by using the modular nuclearity condition of Buchholz, d{\rq}Antoni and Longo. Besides a model-independent result regarding the Reeh-Schlieder property of the vacuum in this framework, an infinite class of quantum field theoretic models with non-trivial interaction is constructed. This construction completes a program initiated by Schroer in a large family of theories, a particular example being the Sinh-Gordon model. The crucial problem of establishing the existence of local observables in these models is solved by verifying the modular nuclearity condition, which here amounts to a condition on analytic properties of form factors of observables localized in wedge regions. It is shown that the constructed models solve the inverse scattering problem for the considered class of S-matrices. Moreover, a proof of asymptotic completeness is obtained by explicitly computing total sets of scattering states. Thestructure of these collision states is found to be in agreement with the heuristic formulae underlying the Zamolodchikov-Faddeev algebra.},
2914         author = {G. Lechner},
2915         doi = {10.1007/s00220-007-0381-5},
2916         eprint = {math-ph/0601022},
2917         journal = {Commun. Math. Phys.},
2918         localfile = {2007 - Lechner - Construction of Quantum Field Theories with Factorizing S-matrices.pdf},
2919         pages = {821--860},
2920         slaccitation = {\%\%CITATION = MATH-PH/0601022\\;\%\%},
2921         title = {{Construction of Quantum Field Theories with Factorizing {S}-Matrices}},
2922         url = {http://arxiv.org/abs/math-ph/0601022},
2923         volume = {277},
2924         x-color = {#199bff},
2925         year = {2008}
2926 }
2927 
2928 @article{Schroer:1997-1,
2929         author = {B. Schroer},
2930         eprint = {hep-th/9702145},
2931         journal = {Nucl. Phys.},
2932         localfile = {1997 - Schroer - Modular Localization and the Bootstrap-Formfactor Program.pdf},
2933         pages = {547--568},
2934         slaccitation = {\%\%CITATION = HEP-TH/9702145\\;\%\%},
2935         title = {{Modular localization and the bootstrap-formfactor program}},
2936         url = {http://arxiv.org/abs/hep-th/9702145v1},
2937         volume = {B499},
2938         year = {1997}
2939 }
2940 
2941 @article{SeibergWitten:1999,
2942         abstract = {We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This change of variables is checked by comparing the ordinary Dirac-Born-Infeld theory with its noncommutative counterpart. We obtain a new perspective on noncommutative gauge theory on a torus, its T-duality, and Morita equivalence. We also discuss the D0/D4 system, the relation to M-theory in DLCQ, and a possible noncommutative version of the six-dimensional (2,0) theory.},
2943         author = {N. Seiberg and E. Witten},
2944         eprint = {hep-th/9908142},
2945         journal = {JHEP},
2946         localfile = {1999 - Seiberg, Witten - String theory and noncommutative geometry.pdf},
2947         pages = {032},
2948         slaccitation = {\%\%CITATION = HEP-TH/9908142\\;\%\%},
2949         title = {{String theory and noncommutative geometry}},
2950         url = {http://arxiv.org/abs/hep-th/9908142},
2951         volume = {09},
2952         year = {1999}
2953 }
2954 
2955 @book{Smirnov:1992,
2956         address = {Singapore},
2957         author = {F. A. Smirnov},
2958         publisher = {World Scientific},
2959         title = {{Form Factors in Completely Integrable Models of Quantum Field Theory}},
2960         year = {1992}
2961 }
2962 
2963 @article{Szabo:2003,
2964         abstract = {A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang-Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study of the gauge group of noncommutative Yang-Mills theory. Some of the more mathematical ideas and techniques of noncommutative geometry are also briefly explained.},
2965         author = {R. J. Szabo},
2966         eprint = {hep-th/0109162},
2967         journal = {Phys. Rept.},
2968         keywords = {NCQFT},
2969         localfile = {2003 - Szabo - Quantum field theory on noncommutative spaces.pdf},
2970         pages = {207--299},
2971         slaccitation = {\%\%CITATION = HEP-TH/0109162\\;\%\%},
2972         title = {{Quantum field theory on noncommutative spaces}},
2973         url = {http://arxiv.org/abs/hep-th/0109162},
2974         volume = {378},
2975         year = {2003}
2976 }
2977 
2978 @book{StreaterWightman:1964,
2979         address = {Reading, MA},
2980         author = {R. F. Streater and A. Wightman},
2981         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Streater R.F., Wightman A.S. PCT, spin and statistics and all that (Benjamin, 1964)(T)(189s)_PQft_.djvu},
2982         publisher = {Benjamin-Cummings},
2983         title = {{PCT, Spin and Statistics, and All That}},
2984         year = {1964}
2985 }
2986 
2987 @article{EliezerWoodard:1989,
2988         author = {D. A. Eliezer and R. P. Woodard},
2989         journal = {Nucl. Phys.},
2990         pages = {389},
2991         slaccitation = {\%\%CITATION = NUPHA,B325,389\\;\%\%},
2992         title = {{The Problem of Nonlocality in String Theory}},
2993         volume = {B325},
2994         year = {1989}
2995 }
2996 
2997 @article{Kawahigashi:2007,
2998         abstract = {We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.},
2999         author = {Y. Kawahigashi},
3000         eprint = {arXiv:0704.0097 [math-ph]},
3001         localfile = {2007 - Kawahigashi - Conformal Field Theory and Operator Algebras.pdf},
3002         slaccitation = {\%\%CITATION = ARXIV:0704.0097\\;\%\%},
3003         title = {{Conformal Field Theory and Operator Algebras}},
3004         url = {http://arxiv.org/abs/0704.0097},
3005         year = {2007}
3006 }
3007 
3008 @article{HalvorsonMger:2006,
3009         abstract = {Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by S. Doplicher, R. Haag, and J. E. Roberts (DHR); and we give an alternative proof of Doplicher and Roberts' reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix.},
3010         author = {H. Halvorson and M. M{\"{u}}ger},
3011         eprint = {math-ph/0602036},
3012         localfile = {2006 - Halvorson, M\"{u}ger - Algebraic Quantum Field Theory.pdf},
3013         slaccitation = {\%\%CITATION = MATH-PH/0602036\\;\%\%},
3014         title = {{Algebraic quantum field theory}},
3015         url = {http://arxiv.org/abs/math-ph/0602036},
3016         year = {2006}
3017 }
3018 
3019 @article{Kawahigashi:2002,
3020         abstract = {We give an exposition on the current status of classification of operator algebraic conformal field theories. We explain roles of complete rationality and alpha-induction for nets of subfactors in such a classification and present the current classification result, a joint work with R. Longo, for the case with central charge less than 1, where we have a complete classification list consisting of the Virasoro nets, their simple current extensions of index 2, and four exceptionals. Two of the four exceptionals appear to be new.},
3021         author = {Y. Kawahigashi},
3022         eprint = {math/0211141},
3023         localfile = {2002 - Kawahigashi - Classification of operator algebraic conformal field theories.pdf},
3024         slaccitation = {\%\%CITATION = MATH/0211141\\;\%\%},
3025         title = {{Classification of operator algebraic conformal field theories}},
3026         url = {http://arxiv.org/abs/math/0211141},
3027         year = {2002}
3028 }
3029 
3030 @article{Davidson:1996,
3031         abstract = {Certain criteria are demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms of that algebra. These are then used to establish a converse to recent results of Borchers and of Wiesbrock on certain one-parameter semigroups of endomorphisms of von Neumann algebras (specifically, Type III\_1 factors) that appear as lightlike translations in the theory of algebras of local observables.},
3032         author = {D. R. Davidson},
3033         eprint = {hep-th/9412094},
3034         journal = {Lett. Math. Phys.},
3035         localfile = {1996 - Davidson - Endomorphism semigroups and lightlike translations.pdf},
3036         pages = {77--90},
3037         slaccitation = {\%\%CITATION = HEP-TH/9412094\\;\%\%},
3038         title = {{Endomorphism semigroups and lightlike translations}},
3039         url = {http://arxiv.org/abs/hep-th/9412094},
3040         volume = {38},
3041         year = {1996}
3042 }
3043 
3044 @article{Svegstrup:2007,
3045         abstract = {In algebraic quantum field theory we consider nets of von Neumann algebras indexed over regions of the space-time. Wiesbrock has shown that strongly additive nets of von Neumann algebras on the circle are in correspondence with standard half-sided modular inclusions. We show that a finite index endomorphism on a half-sided modular inclusion extends to a finite index endomorphism on the corresponding net of von Neumann algebras on the circle. Moreover, we present another approach to encoding endomorphisms on nets of Neumann algebras on the circle into half-sided modular inclusions. There is a natural way to associate a weight to a Moebius covariant endomorphism. The properties of this weight has been studied by Bertozzini, Conti and Longo. In this paper we show the converse, namely how to associate a Moebius covariant endomorphism to a given weight under certain assumptions, thus obtaining a correspondence between a class of weights on a half-sided modular inclusion and a subclass of the Moebius covariant endomorphisms on the associated net of von Neumann algebras. This allows us to treat Moebius covariant endomorphisms in terms of weights on half-sided modular inclusions. As our aim is to provide a framework for treating endomorphisms on nets of von Neumann algebras in terms of the apparently simpler objects of weights on half-sided modular inclusions, we lastly give some basic results for manipulations with such weights.},
3046         author = {R. D. Svegstrup},
3047         journal = {Preprint},
3048         localfile = {2007 - Svegstrup - Endomorphisms on Half-Sided Modular Inclusions.pdf},
3049         title = {{Endomorphisms on Half-Sided Modular Inclusions}},
3050         url = {http://arxiv.org/abs/math-ph/0610027},
3051         year = {2007}
3052 }
3053 
3054 @article{Wiesbrock:1993-2,
3055         abstract = {Let ... be a von Neumann algebras on a Hilbert space , f a common cyclic and separating vector. Assume f to be cyclic and also separating for ... . Denote by ... the modular operators to ... . Assume now ... for all t ~> 0. (Such type of inclusions are called half-sided modular.) Then the modular groups ...... generate a unitary representation of the group SL2Z of positive energy. Another result is related to two half-sided modular inclusions ... and ... . Under proper conditions the three modular groups ... generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.},
3056         author = {H.W. Wiesbrock},
3057         journal = {Lett. Math. Phys.},
3058         localfile = {1993 - Wiesbrock - Symmetries and half-sided modular inclusions of von Neumann algebras.pdf},
3059         pages = {107--114},
3060         title = {{Symmetries and half-sided modular inclusions of von Neumann algebras}},
3061         volume = {28},
3062         year = {1993}
3063 }
3064 
3065 @article{BabujianKarowski:2002,
3066         abstract = {A general model independent approach using the `off-shell Bethe Ansatz' is presented to obtain an integral representation of generalized form factors. The general techniques are applied to the quantum sine-Gordon model alias the massive Thirring model. Exact expressions of all matrix elements are obtained for several local operators. In particular soliton form factors of charge-less operators as for example all higher currents are investigated. It turns out that the various local operators correspond to specific scalar functions called p-functions. The identification of the local operators is performed. In particular the exact results are checked with Feynman graph expansion and full agreement is found. Furthermore all eigenvalues of the infinitely many conserved charges are calculated and the results agree with what is expected from the classical case. Within the frame work of integrable quantum field theories a general model independent `crossing' formula is derived. Furthermore the `bound state intertwiners' are introduced and the bound state form factors are investigated. The general results are again applied to the sine-Gordon model. The integrations are performed and in particular for the lowest breathers a simple formula for generalized form factors is obtained.},
3067         author = {H. M. Babujian and M. Karowski},
3068         eprint = {hep-th/0105178},
3069         journal = {Nucl. Phys.},
3070         localfile = {2001 - Babujian, Karowski - Exact form factors in integrable quantum field theories: the sine-Gordon model (II).pdf},
3071         pages = {407--455},
3072         slaccitation = {\%\%CITATION = HEP-TH/0105178\\;\%\%},
3073         title = {{Exact form factors in integrable quantum field theories: The sine-Gordon model. II}},
3074         url = {http://arxiv.org/abs/hep-th/0105178},
3075         volume = {B620},
3076         year = {2002}
3077 }
3078 
3079 @article{BabujianFoersterKarowski:2006,
3080         abstract = {The purpose of the ''bootstrap program'' for integrable quantum field theories in 1+1 dimensions is to construct explicitly a model in terms of its Wightman functions. In this article, this program is mainly illustrated in terms of the sinh-Gordon model and the SU(N) Gross-Neveu model. The nested off-shell Bethe ansatz for an SU(N) factorizing S-matrix is constructed. We review some previous results on sinh-Gordon form factors and the quantum operator field equation. The problem of how to sum over intermediate states is considered in the short distance limit of the two point Wightman function for the sinh-Gordon model.},
3081         author = {H. M. Babujian and Angela Foerster and M. Karowski},
3082         journal = {SIGMA},
3083         keywords = {High Energy Physics - Theory (hep-th)},
3084         localfile = {2006 - Babujian, Foerster, Karowski - The Form Factor Program: a Review and New Results - the Nested SU(N) Off-Shell Bethe Ansatz.pdf},
3085         pages = {082},
3086         pdf = {http://arxiv.org/pdf/hep-th/0609130},
3087         title = {{The Form Factor Program: a Review and New Results - the Nested SU(N) Off-Shell Bethe Ansatz}},
3088         url = {http://arxiv.org/abs/hep-th/0609130},
3089         v1descr = {Tue, 19 Sep 2006 14:57:02 GMT (22kb)},
3090         v1url = {http://www.arxiv.org/abs/hep-th/0609130v1},
3091         v2descr = {Fri, 29 Sep 2006 09:05:21 GMT (22kb)},
3092         v2url = {http://www.arxiv.org/abs/hep-th/0609130v2},
3093         v3descr = {Thu, 16 Nov 2006 13:36:53 GMT (23kb)},
3094         v3url = {http://www.arxiv.org/abs/hep-th/0609130v3},
3095         v4descr = {Thu, 23 Nov 2006 15:02:55 GMT (24kb)},
3096         volume = {2},
3097         year = {2006}
3098 }
3099 
3100 @article{BahnsDoplicherFredenhagenPiacitelli:2003,
3101         abstract = {We discuss a formulation of quantum field theory on quantum space time where the perturbation expansion of the S-matrix is term by term ultraviolet finite. The characteristic feature of our approach is a quantum version of the Wick product at coinciding points: the differences of coordinates q\_j - \q\_k are not set equal to zero, which would violate the commutation relation between their components. We show that the optimal degree of approximate coincidence can be defined by the evaluation of a conditional expectation which replaces each function of\ q\_j \- q\_k by its expectation value in optimally localized states, while leaving the mean coordinate\s (q\_1 + ..\. + q\_n)/n invariant. The resulting procedure is to a large extent unique, and is invariant under translations and rotations, but violates Lorentz invariance. Indeed, optimal localization refers to a specific Lorentz frame, where the electric and magnetic parts of the commutator of the coordinates have to coincide *). Employing an adiabatic switching, we show that the S-matrix is term by term finite. The matrix elements of the transfer matrix are determined, at each order in the perturbative expansion, by kernels with Gaussian decay in the Planck scale. The adiabatic limit and the large scale limit of this theory will be studied elsewhere. -- *) S. Doplicher, K. Fredenhagen, and J.E.Roberts, Commun. Math. Phys. 172, 187 (1995) [arXiv:hep-th/0303037]},
3102         author = {D. Bahns and S. Doplicher and K. Fredenhagen and G. Piacitelli},
3103         eprint = {hep-th/0301100},
3104         journal = {Commun. Math. Phys.},
3105         keywords = {NCQFT},
3106         localfile = {2003 - Bahns, Doplicher, Fredenhagen, Piacitelli - Ultraviolet Finite Quantum Field Theory on Quantum Spacetime.pdf},
3107         pages = {221--241},
3108         slaccitation = {\%\%CITATION = HEP-TH/0301100\\;\%\%},
3109         title = {{Ultraviolet finite quantum field theory on quantum spacetime}},
3110         url = {http://arxiv.org/abs/hep-th/0301100},
3111         volume = {237},
3112         year = {2003}
3113 }
3114 
3115 @article{BalachandranMarquesQueirozTeotonioSobrinho:2007,
3116         abstract = {Whenever the group $\R^n$ acts on an algebra $\calA$, there is a method to twist $\cal A$ to a new algebra $\calA_\theta$ which depends on an antisymmetric matrix $\theta$ ($\theta^{\mu \nu}=-\theta^{\nu \mu}=\mathrm{constant}$). The Groenewold-Moyal plane $\calA_\theta(\R^{d+1})$ is an example of such a twisted algebra. We give a general construction to realise this twist in terms of $\calA$ itself and certain ``charge'' operators $Q_\mu$. For $\calA_\theta(\R^{d+1})$, $Q_\mu$ are translation generators. This construction is then applied to twist the oscillators realising the Kac-Moody (KM) algebra as well as the KM currents. They give different deformations of the KM algebra. From one of the deformations of the KM algebra, we construct, via the Sugawara construction, the Virasoro algebra. These deformations have implication for statistics as well.},
3117         author = {A. P. Balachandran and A. M. Marques and A. R. Queiroz and P. Teotonio-Sobrinho},
3118         eprint = {hep-th/0608081},
3119         journal = {J. Phys.},
3120         keywords = {NCQFT},
3121         localfile = {2007 - Balachandran, Queiroz, Marques, Teotonio-Sobrinho - Deformed Kac-Moody and Virasoro Algebras.pdf},
3122         pages = {7789--7802},
3123         slaccitation = {\%\%CITATION = HEP-TH/0608081\\;\%\%},
3124         title = {{Deformed Kac-Moody and Virasoro algebras}},
3125         url = {http://arxiv.org/abs/hep-th/0608081},
3126         volume = {A40},
3127         year = {2007}
3128 }
3129 
3130 @article{BalachandranQueirozMarquesTeotonioSobrinho:2007,
3131         abstract = {Quantum field theories (QFT's) on noncommutative spacetimes are currently under intensive study. Usually such theories have world sheet noncommutativity. In the present work, instead, we study QFT's with commutative world sheet and noncommutative target space. Such noncommutativity can be interpreted in terms of twisted statistics and is related to earlier work of Oeckl [1], and others [2,3,4,5,6,7,8]. As an application, we analyse here free scalar field theories with the noncommutative plane as target space, and find the twisted spectra of their free Hamiltonians. The Hamiltonians of such free field theories contain an extra term proportional to a $z$-component angular momentum, resembling a coupling with a magnetic field. We analyse the energy spectrum of one such typical theory, and find that it is split (an effect similar to the Zeeman effect). Its partition function leads to a deformed black body spectrum, which is analysed in detail. The difference between the usual and the deformed black-body spectrum appears in the region of high frequence photons. Therefore we expect that the deformed black-body radiation may potentially be used to compute a GZK cut-off which will depend on the noncommutative parameter $\theta$.},
3132         author = {A. P. Balachandran and A. R. Queiroz and A. M. Marques and P. Teotonio-Sobrinho},
3133         comments = {Derivation of a deformed blackbody radiation spectrum in theories with ``worldsheet noncommutativity''.},
3134         druck = {Booklet 24.07.08},
3135         eprint = {arXiv:0706.0021 [hep-th]},
3136         keywords = {Lesen; NCQFT},
3137         lesen = {X},
3138         localfile = {2007 - Balachandran, Queiroz, Marques, Teotonio-Sobrinho - Quantum Fields with Noncommutative Target Spaces.pdf},
3139         slaccitation = {\%\%CITATION = ARXIV:0706.0021\\;\%\%},
3140         title = {{Quantum Fields with Noncommutative Target Spaces}},
3141         url = {http://arxiv.org/abs/0706.0021},
3142         year = {2007}
3143 }
3144 
3145 @article{BisognanoWichmann:1976,
3146         author = {J. J Bisognano and E. H. Wichmann},
3147         journal = {J. Math. Phys.},
3148         localfile = {1976 - Bisognano, Wichmann - On the Duality Condition for Quantum Fields.pdf},
3149         pages = {303--321},
3150         slaccitation = {\%\%CITATION = JMAPA,17,303\\;\%\%},
3151         title = {{On the Duality Condition for Quantum Fields}},
3152         volume = {17},
3153         year = {1976}
3154 }
3155 
3156 @article{BisognanoWichmann:1975,
3157         author = {J. J Bisognano and E. H. Wichmann},
3158         journal = {J. Math. Phys.},
3159         localfile = {1974 - Bisognano, Wichmann - On the Duality Condition for a Hermitian Quantum Field.pdf},
3160         pages = {985--1007},
3161         slaccitation = {\%\%CITATION = JMAPA,16,985\\;\%\%},
3162         title = {{On the Duality Condition for a Hermitian Scalar Field}},
3163         volume = {16},
3164         year = {1975}
3165 }
3166 
3167 @article{Arzano:2007,
3168         abstract = {We study the action of space-time symmetries on quantum fields in the presence of small departures from locality determined by dynamical gravity. It is shown that, under such relaxation of locality, the symmetries of the theory cannot be described within the usual framework of Lie algebras but rather in terms of non-co-commutative Hopf algebras or "quantum groups". Similar "quantizations" of space-time symmetries are expected to emerge in the low-energy limit of certain quantum gravity models and have been used to describe the symmetries of various non-commutative space-times. Our result provides an intuitive characterization of the mechanism that could lead to the emergence of deformed co-products in models of quantum relativistic symmetries.},
3169         author = {M. Arzano},
3170         journal = {Phys. Rev. D},
3171         keywords = {High Energy Physics - Theory (hep-th)},
3172         pages = {025013},
3173         pdf = {http://arxiv.org/pdf/0710.1083},
3174         title = {{Quantum fields, non-locality and quantum group symmetries}},
3175         url = {http://arxiv.org/abs/0710.1083},
3176         v1descr = {Fri, 5 Oct 2007 17:17:03 GMT (12kb)},
3177         v1url = {http://www.arxiv.org/abs/0710.1083v1},
3178         v2descr = {Fri, 8 Feb 2008 20:56:29 GMT (12kb)},
3179         volume = {77},
3180         year = {2008}
3181 }
3182 
3183 @article{Borchers:1999,
3184         abstract = {For a von Neumann algebra with a cyclic and separating vector it will be shown that the von Neumann subalgebras with the same cyclic vector can uniquely be characterized by one-parametric operator-valued functions obeying a set of conditions. Since the properties contain no reference to the subalgebra these operator-valued functions will be called characteristic functions. On the set of characteristic functions there exists a natural topology under which this set is complete.},
3185         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
3186         journal = {Commun. Math. Phys.},
3187         localfile = {1999 - Borchers - On the embedding of von Neumann subalgebras.pdf},
3188         pages = {69--79},
3189         title = {{On the embedding of von Neumann subalgebras}},
3190         volume = {205},
3191         year = {1999}
3192 }
3193 
3194 @article{Borchers:1997,
3195         abstract = {Given a von Neumann algebra M with cyclic and separating vector OHgr and with the modular group deltait which is associated with the pair (M, OHgr) we will investigate the von Neumann subalgebras N sub M which fulfil the principle of half-sided modular inclusion. We show that this set is almost a lattice with respect to intersection and union. Furthermore, in this set we can introduce an equivalence relation respecting the lattice structure. To every von Neumann subalgebra fulfilling the condition of half-sided modular inclusion is associated a unique one-parametric translation group which fulfils the spectrum condition. Within this setting, one deals with two orders, the order of inclusion of subalgebras, and the order of positive operators between the generators of the translations. The first order implies the reverse of the second but the converse holds only if the corresponding translations commute.},
3196         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
3197         journal = {Lett. Math. Phys.},
3198         localfile = {1997 - Borchers - On the Lattice of Subalgebras Associated with the Principle of Half-sided Modular Inclusion.pdf},
3199         number = {4},
3200         pages = {371--390},
3201         title = {{On the Lattice of Subalgebras Associated with the Principle of Half-sided Modular Inclusion}},
3202         url = {http://www.springerlink.com/content/un027304k4m253q7/?p=1a14bec3579d46e3a219897d6845164b&pi=5},
3203         volume = {40},
3204         year = {1997}
3205 }
3206 
3207 @article{Borchers:1996,
3208         abstract = {In this note we will give a construction of the Poincar\'{e} group out of the modular groups of the wedge algebras provided the groups act on the algebra of every double cone like the associated Lorentz boosts. This construction will use the concept of half-sided modular inclusions instead of the first and second cohomology of the Poincar\'{e} group as used by Brunetti, Guido and Longo. By our method we obtain directly the Poincar\'{e} group and not its covering group.},
3209         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
3210         journal = {Commun. Math. Phys.},
3211         localfile = {1996 - Borchers - Half-sided modular inclusion and the construction of the Poincare group.pdf},
3212         pages = {703--723},
3213         title = {{Half-sided modular inclusion and the construction of the Poincar\'{e} group}},
3214         url = {http://www.springerlink.com/content/pn7wp853n1666537/?p=98c19fdbd87648f79f623d3d44e9bf70&pi=8},
3215         volume = {179},
3216         year = {1996}
3217 }
3218 
3219 @article{ArakiZsido:2005,
3220         abstract = {A result of H.-W. Wiesbrock is extended from the case of a common cyclic and separating vector for the half-sided modular inclusion N ⊂ M of von Neumann algebras to the case of a common faithful normal semi-finite weight and at the same time a gap in Wiesbrock's proof is filled in.},
3221         author = {H. Araki and L. Zsido},
3222         journal = {Rev. Math. Phys.},
3223         localfile = {2005 - Araki, Zsido - Extension of the structure theorem of Borchers and its application to half-sided modular inclusions.pdf},
3224         pages = {491--543},
3225         title = {{Extension of the structure theorem of {B}orchers and its application to half-sided modular inclusions}},
3226         volume = {17},
3227         year = {2005}
3228 }
3229 
3230 @misc{ChenFrhlichPizzo:2007,
3231         abstract = {We construct infraparticle scattering states for Compton scattering in the standard model of non-relativistic QED. In our construction, an infrared cutoff initially introduced to regularize the model is removed completely. We rigorously establish the properties of infraparticle scattering theory predicted in the classic work of Bloch and Nordsieck from the 1930's, Faddeev and Kulish, and others. Our results represent a basic step towards solving the infrared problem in (non-relativistic) QED.},
3232         author = {T. Chen and J. Froehlich and A. Pizzo},
3233         keywords = {Mathematical Physics (math-ph)},
3234         month = jul,
3235         pdf = {http://arxiv.org/pdf/0709.2493},
3236         title = {{Infraparticle Scattering States in Non-Relativistic QED: I. The Bloch-Nordsieck Paradigm}},
3237         url = {http://arxiv.org/abs/0709.2493},
3238         v1descr = {Sun, 16 Sep 2007 13:43:38 GMT (166kb)},
3239         v1url = {http://www.arxiv.org/abs/0709.2493v1},
3240         v2descr = {Mon, 27 Jul 2009 19:27:25 GMT (165kb)},
3241         year = {2009}
3242 }
3243 
3244 @article{GabbianiFrhlich:1993,
3245         author = {F. Gabbiani and J. Fr{\"{o}}hlich},
3246         journal = {Commun. Math. Phys.},
3247         localfile = {1993 - Fr\"{o}hlich, Gabbiani - Operator algebras and conformal field theory.pdf},
3248         pages = {569--640},
3249         slaccitation = {\%\%CITATION = CMPHA,155,569\\;\%\%},
3250         title = {{Operator algebras and conformal field theory}},
3251         volume = {155},
3252         year = {1993}
3253 }
3254 
3255 @article{Jkel:1999,
3256         abstract = {We establish the Schlieder and the Borchers property for thermal field theories. In addition, we provide some information on the commutation and localization properties of projection operators.},
3257         author = {C. D. J{\"{a}}kel},
3258         journal = {J. Math. Phys.},
3259         localfile = {1999 - J\"{a}kel - Two algebraic properties of thermal quantum field theories.pdf},
3260         number = {12},
3261         pages = {6234--6244},
3262         title = {{Two algebraic properties of thermal quantum field theories}},
3263         volume = {40},
3264         year = {1999}
3265 }
3266 
3267 @article{Araki:1963,
3268         author = {H. Araki},
3269         journal = {J. Math. Phys.},
3270         localfile = {1963 - Araki - A Lattice of Von Neumann Algebras Associated with the Quantum Theory of a Free Bose Field.pdf},
3271         number = {11},
3272         pages = {1343--1362},
3273         title = {{A Lattice of von {N}eumann algebras Associated with the Quantum Theory of a Free {B}ose Field}},
3274         volume = {4},
3275         year = {1963}
3276 }
3277 
3278 @article{Licht:1963,
3279         author = {A. L. Licht},
3280         journal = {J. Math. Phys.},
3281         localfile = {1963 - Licht - Strict Localization.pdf},
3282         number = {11},
3283         pages = {1443--1447},
3284         title = {{Strict Localization}},
3285         volume = {4},
3286         year = {1963}
3287 }
3288 
3289 @article{Araki:1964,
3290         author = {H. Araki},
3291         journal = {J. Math. Phys.},
3292         localfile = {1964 - Araki - Von Neumann Algebras of Local Observables for Free Scalar Field.pdf},
3293         number = {1},
3294         pages = {1--13},
3295         title = {{Von {N}eumann Algebras of Local Observables for Free Scalar Field}},
3296         volume = {5},
3297         year = {1964}
3298 }
3299 
3300 @article{Borchers:1965,
3301         abstract = {The usual investigations of the connection of spin and statistics start with the hypothesis that there exist only fields either commuting or anti-commuting for spacelike separations. Starting from local rings of measurements we want to show that this hypothesis can be added without loss of generality.},
3302         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
3303         journal = {Commun. Math. Phys.},
3304         localfile = {1965 - Borchers - Local rings and the connection of spin with statistics.pdf},
3305         pages = {281--307},
3306         title = {{Local Rings and the Connection of Spin with Statistics}},
3307         volume = {1},
3308         year = {1965}
3309 }
3310 
3311 @article{Borchers:1965-1,
3312         abstract = {The global structure analysis of local field operators is reinvestigated.},
3313         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
3314         journal = {Commun. Math. Phys.},
3315         localfile = {1965 - Borchers - On the structure of the algebra of field operators. II.pdf},
3316         pages = {49--56},
3317         title = {{On the Structure of the Algebra of Field Operators II}},
3318         volume = {1},
3319         year = {1965}
3320 }
3321 
3322 @article{Borchers:1965-2,
3323         abstract = {We want to construct, for every local irreducible quantum field theory which fulfils the spectrum condition, a new theory with the properties: 1) It is physically equivalent to the given theory (in the sense of HAAG and KASTLER). 2) The representation space contains a vacuum state. 3) The new theory satisfies the spectrum condition. 4) For every bounded region O the two representations of the algebra A(O) are unitarily equivalent. 5) The new theory is uniquely characterized by the properties 1)-----------------------------------------------------------------------------4).},
3324         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
3325         journal = {Commun. Math. Phys.},
3326         localfile = {1965 - Borchers - On the vacuum state in quantum field theory II.pdf},
3327         pages = {57--79},
3328         title = {{On the Vacuum State in Quantum Field Theory II}},
3329         volume = {1},
3330         year = {1965}
3331 }
3332 
3333 @article{BrosEpsteinGlaser:1965,
3334         abstract = {In the framework of the \&.6f.2£. formalism, the crossing property is proved on the mass shell for amplitudes involving two incoming and two outgoing stable particles with arbitrary masses. Any couple of physical regions in the (s, t, u) plane corresponding to crossed processes are shown to be connected by a certain domain of analyticity. For every negative value of ί, the amplitude is analytic in the cut s-plane outside of a large circle.},
3335         author = {J. Bros and H. Epstein and V. Glaser},
3336         journal = {Commun. Math. Phys.},
3337         localfile = {1965 - Bros, Epstein, Glaser - A proof of the crossing property for two-particle amplitudes in general quantum field theory.pdf},
3338         pages = {240--264},
3339         title = {{A Proof of the Crossing Property for Two-Particle-Amplitudes in General Quantum Field Theory }},
3340         volume = {1},
3341         year = {1965}
3342 }
3343 
3344 @article{BirkeFrhlich:2002,
3345         abstract = {A general form of the ``Wick rotation'', starting from imaginary-time Green functions of quantum-mechanical systems in thermal equilibrium at positive temperature, is established. Extending work of H. Araki, the role of the KMS condition and of an associated anti-unitary symmetry operation, the ``modular conjugation'', in constructing analytic continuations of Green functions from real- to imaginary times, and back, is clarified. The relationship between the KMS condition for the vacuum with respect to Lorentz boosts, on one hand, and the spin-statistics connection and the PCT theorem, on the other hand, in local, relativistic quantum field theory is recalled. General results on the reconstruction of local quantum theories in various nontrivial gravitational backgrounds from ``Euclidian amplitudes'' are presented. In particular, a general form of the KMS condition is proposed and applied, e.g., to the Unruh- and the Hawking effects.},
3346         author = {L. Birke and J. Fr{\"{o}}hlich},
3347         eprint = {math-ph/0204023},
3348         journal = {Rev. Math. Phys.},
3349         localfile = {2002 - Birke, Fr\"{o}hlich - KMS, etc.pdf},
3350         pages = {829--872},
3351         slaccitation = {\%\%CITATION = MATH-PH/0204023\\;\%\%},
3352         title = {{KMS, etc}},
3353         volume = {14},
3354         year = {2002}
3355 }
3356 
3357 @article{HaagSwieca:1965,
3358         abstract = {We give a criterion which has to be satisfied in a Quantum Field Theory in order to allow a complete particle interpretation of the theory. The notion of ``essentially localized states'' in Field Theory is re-examined.},
3359         author = {R. Haag and J. A. Swieca},
3360         journal = {Commun. Math. Phys.},
3361         localfile = {1965 - Haag, Swieca - When does a quantum field theory describe particles.pdf},
3362         pages = {308--320},
3363         title = {{When does a Quantum Field Theory Describe Particles?}},
3364         volume = {1},
3365         year = {1965}
3366 }
3367 
3368 @article{Jaffe:1965,
3369         abstract = {Perturbation theory is studied in two dimensional space-time. There all non-derivative boson self-interactions are renormalizable and in each order of perturbation theory there are no divergences, that is all renormalizations are finite in perturbation theory. Thus the unrenormalized perturbation series may be oo studied and it is shown that any interaction of the general form ... leads to Green's functions which are not analytic in A at A = 0. This result holds in momentum space at a large set of points, enough to show that the Green's functions are not distributions in the momenta which are analytic in A at A = 0. Furthermore the proper self energy and the two-particle scattering amplitude are shown not to be analytic in A at A = 0 for certain momenta on or below the bare mass shell. In the course of this analysis we use the integral representations for Feynman graphs to derive a minorization of the form ... > A Bnior the contribution from all nth order connected graphs in a theory with an interaction of the form Hj(x) = .... Then the constants A and B depend only on ... the momenta ... and not on the structure of a particular graph.},
3370         author = {A. Jaffe},
3371         journal = {Commun. Math. Phys.},
3372         localfile = {1965 - Jaffe - Divergence of perturbation theory for bosons.pdf},
3373         pages = {127--149},
3374         title = {{Divergence of Perturbation Theory for Bosons}},
3375         volume = {1},
3376         year = {1965}
3377 }
3378 
3379 @article{Kastler:1965,
3380         abstract = {We give a systematic description of several *-algebras associated with a free Boson field. In this first part the structure of the one-particle space enters only through its symplectic form σ and a directed absorbing set of finite-dimensional subspaces on which σ is non-degenerate. The Banach *-algebras ... and ... of absolutely continuous resp. bounded measures on a finite-dimensional symplectic space ..., with their ``twisted convolution product'' stemming from Weyls commutation relations, are studied as the analogues of the £PX resp. JHX algebras of a locally compact group. The fundamental ``vacuum idempotent'' Ω determines their (unique) Schrodinger representation, Schrόdinger Jl*-norm and Sclirodinger C*-completions JS?i((£, or) and J(x^i σ). After a study of these one proceeds to a construction as an inductive limit of the algebras ~^i(§, σ) and ^ x ( § , a) for an infinite-dimensional symplectic space (§, or). The ``Γock representations'' (with the corresponding ``field operators'') are presented as the infinite-dimensional gene- ralization of the Schrodinger representation. The paper ends with a discussion of several possible choices for the ``free Boson <7*-algebra''.},
3381         author = {D. Kastler},
3382         journal = {Commun. Math. Phys.},
3383         localfile = {1965 - Kastler - The Cstar-algebras of a free Boson field. I. Discussion of the basic facts.pdf},
3384         pages = {14--48},
3385         title = {{The C*-Algebras of a Free Boson Field - I. Discussion of the Basic Facts }},
3386         volume = {1},
3387         year = {1965}
3388 }
3389 
3390 @article{LangerholcSchroer:1965,
3391         abstract = {It is shown that the von Neumann algebra ... generated by any scalar local function B(x) of the free field A0(x) is equal either to ... or to .... The latter statement holds if the state space ... obtained from the vacuum state by repeated application of B(x) is orthogonal to the one particle subspace. In the proof of these statements, space-time limiting techniques are used.},
3392         author = {J. Langerholc and B. Schroer},
3393         journal = {Commun. Math. Phys.},
3394         localfile = {1965 - Langerholc, Schroer - On the structure of the von Neumann algebras generated by local functions of the free Bose field.pdf},
3395         pages = {215--239},
3396         title = {{On the Structure of the von Neumann Algebras Generated by Local Functions of the Free Bose Field }},
3397         volume = {1},
3398         year = {1965}
3399 }
3400 
3401 @article{Robinson:1965,
3402         abstract = {It is proved that if the n-point correlation functions of a system vanish for all n > N then they vanish for all n > 2. The theorem is valid for a wide variety of formalisms and an explicit proof is given for a Bose system with the canonical commutation relations a proof is sketched out for a relativistic field theory of the Wightman type. The essential property used in the proof is the positive definite metric.},
3403         author = {D. W. Robinson},
3404         journal = {Commun. Math. Phys.},
3405         localfile = {1965 - Robinson - A theorem concerning the positive metric.pdf},
3406         pages = {89--94},
3407         title = {{A Theorem Concerning the Positive Metric}},
3408         volume = {1},
3409         year = {1965}
3410 }
3411 
3412 @article{Robinson:1965-1,
3413         abstract = {The mathematical formalism describing the Bose gas at zero temperature is analysed with the aid of methods that have recently been successful in relativistic quantum field theory. First the spectrum conditions for an infinitely extended system are given and the algebra of observables and the algebra of field operators are defined. General properties of states over these algebras are discussed and theorems are given which connect the linked cluster property, translation invariance and the purity of the states. It is proved that pure states over the algebra of observables have the property of 'factorisable off-diagonal long range order'. The class of 'quasi free states' is defined and of these states those which are translation invariant and possess the linked cluster property are analysed. It is shown that this class of states contains a subclass of pure states of the Bogoliubov type and a subclass of states which are mixtures of non-translationally invariant pure states. The applications of these 'quasi free states' to the interacting Bose gas are summarized.},
3414         author = {D. W. Robinson},
3415         journal = {Commun. Math. Phys.},
3416         localfile = {1965 - Robinson - The ground state of the Bose gas.pdf},
3417         pages = {159--174},
3418         title = {{The Ground State of the Bose Gas}},
3419         volume = {1},
3420         year = {1965}
3421 }
3422 
3423 @article{Schlieder:1965,
3424         abstract = {For the case of a field theory with a nuclear space of test functions (for instance, the space of strongly decreasing test functions) compact sets of states are constructed; these correspond to sets of localized states. Only such states are considered which are elements of a fixed subspace of the entire Hubert space. This subspace belongs to the m-point functions of order less than a certain fixed 2 n.},
3425         author = {S. Schlieder},
3426         journal = {Commun. Math. Phys.},
3427         localfile = {1965 - Schlieder - Some remarks about the localization of states in a quantum field theory.pdf},
3428         pages = {265--280},
3429         title = {{Some Remarks about the Localization of States in a Quantum Field Theory*}},
3430         volume = {1},
3431         year = {1965}
3432 }
3433 
3434 @article{Borchers:1966,
3435         abstract = {The spectrum condition implies that energy and momentum are limits of local observables.},
3436         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
3437         journal = {Commun. Math. Phys.},
3438         localfile = {1966 - Borchers - Energy and momentum as observables in quantum field theory.pdf},
3439         pages = {49--54},
3440         title = {{Energy and Momentum as Observables in Quantum Field Theory }},
3441         volume = {2},
3442         year = {1966}
3443 }
3444 
3445 @article{DellAntonioDoplicherRuelle:1966,
3446         abstract = {The aim of this note is to characterize representations of the canonical commutation or anticommutation relations which, on a subspace of the ``space of test-functions'', reduce to a sum of copies of the Fock representation.},
3447         author = {{{{{{{{{{{{{{{{{{{{{{{{{{G.-F.}}}}}}}}}}}}}}}}}}}}}}}}} Dell'Antonio and S. Doplicher and D. Ruelle},
3448         journal = {Commun. Math. Phys.},
3449         localfile = {1966 - Dell'Antonio, Doplicher, Ruelle - A theorem on canonical commutation and anticommutation relations.pdf},
3450         pages = {223--230},
3451         title = {{A Theorem on Canonical Commutation and Anticommutation Relations }},
3452         volume = {2},
3453         year = {1966}
3454 }
3455 
3456 @article{DoplicherKastlerRobinson:1966,
3457         abstract = {Starting from a G^-algebra 21 and a locally compact group T of automorphisms of 21 we construct a ``covariance algebra'' 21^ with the property that the corresponding *-representations are in one-to-one correspondence with covariant representations of 21 i.e. *-representations of 21 in which the automor- phisms are continuously unitarily implemented. We further construct for rela- tivistic field theory an algebra 2ί^(F) yielding the \\\\# -representations of 21 in which the space time translations have their spectrum contained in V. The problem of denumerable occurence of superselection sectors is formulated as a condition on the spectrum of 2ί^(F). Finally we consider the covariance algebra 21 £ built with space translations alone and show its relevance for the discussion of equilibrium states in statistical mechanics, namely we restore in this framework the equiv- alence of uniqueness of the vacuum, irreducibility and a weak clustering property.},
3458         author = {S. Doplicher and D. Kastler and D. W. Robinson},
3459         journal = {Commun. Math. Phys.},
3460         localfile = {1966 - Doplicher, Kastler, Robinson - Covariance algebras in field theory and statistical mechanics.pdf},
3461         pages = {1--28},
3462         title = {{Covariance Algebras in Field Theory and Statistical Mechanics }},
3463         volume = {3},
3464         year = {1966}
3465 }
3466 
3467 @article{KadisonRingrose:1967,
3468         abstract = {The theorem that each derivation of a (7*-algebra 21 extends to an inner derivation of the weak-operator closure φ (2l)~ of 21 in each faithful represen- tation φ of 21 is proved in sketch and used to study the automorphism group of 21 in its norm topology. It is proved that the connected component of the identity i in this group contains the open ball \& of radius 2 with center i and that each auto- morphism in\\ \&\& extends to an inner automorphism of},
3469         author = {R. V. Kadison and J. R. Ringrose},
3470         journal = {Commun. Math. Phys.},
3471         localfile = {1966 - Kadison, Ringrose - Derivations and automorphisms of operator algebras.pdf},
3472         pages = {32--63},
3473         title = {{Derivations and Automorphisms of Operator Algebras }},
3474         volume = {4},
3475         year = {1967}
3476 }
3477 
3478 @article{KastlerRobinsonSwieca:1966,
3479         abstract = {We consider, in the framework of local field theory with translation symmetry, automorphisms connected with locally conserved currents. We show that such automorphisms lead to symmetries, i.e. are implementable by unitary operators, whenever the smallest mass in the theory is non-zero. Therefore we conclude that a ``spontaneously broken symmetry'' is possible only in the event that the smallest mass is zero. This establishes the theorem first conjectured by GOLD STONE.},
3480         author = {D. Kastler and D. W. Robinson and J. A. Swieca},
3481         journal = {Commun. Math. Phys.},
3482         localfile = {1966 - Kastler, Robinson, Swieca - Conserved currents and associated symmetries Goldstone's theorem.pdf},
3483         pages = {108--120},
3484         title = {{Conserved Currents and Associated Symmetries; Goldstone's Theorem}},
3485         volume = {2},
3486         year = {1966}
3487 }
3488 
3489 @article{KupschSandhas:1966,
3490         abstract = {The existence of Moller operators is proved for singular potentials which decrease more rapidly at infinity than the Coulomb potential. The question of their uniqueness is discussed.},
3491         author = {J. Kupsch and W. Sandhas},
3492         journal = {Commun. Math. Phys.},
3493         localfile = {1966 - Kupsch, Sandhas - Moeller operators for scattering on singular potentials.pdf},
3494         pages = {147--154},
3495         title = {{Moller Operators for Scattering on Singular Potentials}},
3496         volume = {2},
3497         year = {1966}
3498 }
3499 
3500 @article{Lehmann:1966,
3501         abstract = {It is shown that scattering amplitudes have analytic properties as functions of momentum transfer not only for physical, but also for complex energies. This follows from local relativistic field theory for all reactions for which an ordinary dispersion relation can be proved. It is further shown that such amplitudes are boundary values of analytic functions of the two variables energy and momentum transfer. A domain of holomorphy ----------------------------------------------------------------------------- which is however not best possible ----------------------------------------------------------------------------- is given explicitly. It follows then that partial waves can be analytically continued to complex energies.},
3502         author = {H. Lehmann},
3503         journal = {Commun. Math. Phys.},
3504         localfile = {1966 - Lehmann - Analytic properties of scattering amplitudes in two variables in general quantum field theory.pdf},
3505         pages = {375--383},
3506         title = {{Analytic Properties of Scattering Amplitudes in two Variables in General Quantum Field Theory }},
3507         volume = {2},
3508         year = {1966}
3509 }
3510 
3511 @article{Licht:1966,
3512         author = {A. L. Licht},
3513         journal = {J. Math. Phys.},
3514         localfile = {1966 - Licht - Local States.pdf},
3515         number = {9},
3516         pages = {1656--1669},
3517         title = {{Local States}},
3518         volume = {7},
3519         year = {1966}
3520 }
3521 
3522 @article{SchroerStichel:1966,
3523         abstract = {In this paper we give a rigorous formulation of Gell-Mann's equal time commutation relations in the framework of general quantum field theory. We show that this can be achieved despite the nonexistence of charge operators for non-conserved currents. Starting from the properly formulated equal time commutation relations of ``generalized charges'', we justify the application of the Gauss-Theorem and we discuss the limits for large times of time dependent ``generalized charges''. The Jost-Lehmann-Dyson representation is used in order to show that the equal time commutation relations always lead to exactly one, frame independent, sum rule. We discuss the connection between properties of the Jost-Lehmann-Dyson spectral function and the convergence of Adler-Weisberger type sum rules.},
3524         author = {B. Schroer and P. Stichel},
3525         journal = {Commun. Math. Phys.},
3526         localfile = {1966 - Schroer, Stichel - Current commutation relations in the framework of general quantum field theory.pdf},
3527         pages = {258--281},
3528         title = {{Current Commutation Relations in the Framework of General Quantum Field Theory }},
3529         volume = {3},
3530         year = {1966}
3531 }
3532 
3533 @article{Streater:1966,
3534         abstract = {The dynamical variables of a classical system form a Lie algebra ©, where the Lie multiplication is given by the Poisson bracket. Following the ideas of SouϊtiAU and SEGAL, but with some modifications, we show that it is possible to realize © as a concrete algebra of smooth transformations of the functionals Φ on the manifold 2!ΐ of smooth solutions to the classical equations of motion. It is even possible to do this in such a way that the action of a chosen dynamical variable, say the Hamiltonian, is given by the classical motion on the manifold, so that the quantum and classical motions coincide. In this realization, constant functionals are realized by multiples of the identity operator. For a finite number of degrees of freedom, n, the space of functionals can be made into a Hubert space Jf using the invariant Liouville volume element the dynamical variables F become operators F in this space. We prove that for any hamiltonian H quadratic in the canonical variables qx... qn> px... pn there exists a subspace ^f x C \& which is invariant under the action of pί9 qk and H, and such that the restriction of j)j, qk to ^>1 form an irreducible set of operators. Therefore, SOTJRIATT'S quantization rule agrees with the usual one for quadratic hamiltonians. In fact, it gives the Bargmann-Segal holo- morphic function realization. For non-linear problems in general, however, the operators pjf qk form a reducible set on any subspace of 3tf invariant under the action of the Hamiltonian. In particular this happens for H = -~-p2 -\- λq^. Therefore, SoTJRiAu's rule cannot agree with the usual quantization procedure for general non-linear systems. The method can be applied to the quantization of a non-linear wave equation and differs from the usual attempts in that (1) at any fixed time the field and its conjugate momentum may form a reducible set (2) the theory is less singular than usual. For a particular wave equation ( • + m2) Φiχ) ----------------------------------------------------------------------------- λ φ3(x), we show heuristically that the interacting field may be defined as a first order differential operator acting on c°°-functions on the manifold of solutions. In order to make this space into a Hubert space, one must define a suitable method of functional integration on the manifold; this problem is discussed, without, however, arriving at a satisfactory conclusion.},
3535         author = {R. F. Streater},
3536         journal = {Commun. Math. Phys.},
3537         localfile = {1966 - Streater - Canonical quantization.pdf},
3538         pages = {354--374},
3539         title = {{Canonical Quantization}},
3540         volume = {2},
3541         year = {1966}
3542 }
3543 
3544 @article{ArakiHaag:1967,
3545         abstract = {Asymptotic relations for matrix elements of quasilocal operators are given which generalize and extend the Lehmann-Symanzik-Zimmermann relations. These relations allow the simulation of a coincidence arrangement of particle detectors in the mathematical frame of the theory and thereby the expression of collision cross sections in terms of expectation values of observables.},
3546         author = {H. Araki and R. Haag},
3547         journal = {Commun. Math. Phys.},
3548         localfile = {1967 - Araki, Haag - Collision cross sections in terms of local observables.pdf},
3549         pages = {77--91},
3550         title = {{Collision Cross Sections in Terms of Local Observables}},
3551         volume = {4},
3552         year = {1967}
3553 }
3554 
3555 @article{Borchers:1967,
3556         abstract = {The two sided ideals of the C*-algebra generated by local v. Neumann algebras are investigated.},
3557         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
3558         journal = {Commun. Math. Phys.},
3559         localfile = {1967 - Borchers - A remark on a theorem of B. Misra.pdf},
3560         pages = {315--323},
3561         title = {{A Remark on a Theorem of B. Misra}},
3562         volume = {4},
3563         year = {1967}
3564 }
3565 
3566 @article{BrosEpsteinGlaser:1967,
3567         abstract = {We prove a conjecture of R. STREATER [1] on the finite covariance of functions holomorphic in the extended tube which are Laplace transforms of two tempered distributions with supports in the future and past cones. A new, slightly more general proof is given for a theorem of analytic completion of [1],},
3568         author = {J. Bros and H. Epstein and V. Glaser},
3569         journal = {Commun. Math. Phys.},
3570         localfile = {1967 - Bros, Epstein, Glaser - On the connection between analyticity and Lorentz covariance of Wightman functions.pdf},
3571         pages = {77--100},
3572         title = {{On the Connection Between Analyticity and Lorentz Covariance of Wightman Functions }},
3573         volume = {6},
3574         year = {1967}
3575 }
3576 
3577 @article{EzawaSwieca:1967,
3578         abstract = {In a relativistic field theory Goldstone's theorem is proved without any assumption about the existence of covariant fields and for arbitrary expectation values.},
3579         author = {H. Ezawa and J. A. Swieca},
3580         journal = {Commun. Math. Phys.},
3581         localfile = {1967 - Ezawa, Swieca - Spontaneous breakdown of symmetries and zero-mass states.pdf},
3582         pages = {330--336},
3583         title = {{Spontaneous Breakdown of Symmetries and Zero-Mass States}},
3584         volume = {5},
3585         year = {1967}
3586 }
3587 
3588 @article{Glimm:1967,
3589         abstract = {A renormalization procedure is proposed. It gives rigorous mathematical meaning to the infinite cancellations in this model. A space cutoff is introduced in the interaction term V and so V has the form f V(x) dx, but there are no momentum cutoffs in V. There is an infinite constant and an infinite boson mass renormalization in this model. The main result is that the renormalized Hamiltonian is rigorously defined as a bilinear form in the Fock Hubert space.},
3590         author = {J. Glimm},
3591         journal = {Commun. Math. Phys.},
3592         localfile = {1967 - Glimm - Yukawa coupling of quantum fields in two dimensions. I.pdf},
3593         pages = {34--86},
3594         title = {{Yukawa Coupling of Quantum Fields in Two Dimensions. I}},
3595         volume = {5},
3596         year = {1967}
3597 }
3598 
3599 @article{HaagHugenholtzWinnink:1967,
3600         abstract = {Representations of the O*-algebra Qi of observables corresponding to thermal equilibrium of a system at given temperature T and chemical potential μ are studied. Both for finite and for infinite systems it is shown that the representa- tion is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of 21 onto its commutant. This means that there is an equivalent anti-linear representation of £1 in the commutant. The relation of these properties with the Kubo-Martin-Schwinger boundary condition is discussed.},
3601         author = {R. Haag and N. M. Hugenholtz and M. Winnink},
3602         journal = {Commun. Math. Phys.},
3603         localfile = {1967 - Haag, Hugenholtz, Winnink - On the equilibrium states in quantum statistical mechanics.pdf},
3604         pages = {215--236},
3605         title = {{On the Equilibrium States in Quantum Statistical Mechanics }},
3606         volume = {5},
3607         year = {1967}
3608 }
3609 
3610 @article{Kadison:1967,
3611         abstract = {It is proved, assuming Einstein causality, that the energy-momentum spectrum of a quantum field cannot be bounded. More is known under special assumptions [1, 4]. Our main concern is the method and general applicability of the result.},
3612         author = {R. V. Kadison},
3613         journal = {Commun. Math. Phys.},
3614         localfile = {1967 - Kadison - The energy momentum spectrum of quantum fields.pdf},
3615         pages = {258--260},
3616         title = {{The Energy Momentum Spectrum of Quantum Fields}},
3617         volume = {4},
3618         year = {1967}
3619 }
3620 
3621 @article{Borchers:1968,
3622         abstract = {It will be shown that the weak additivity-property is not only sufficient but also necessary for the derivation of the Reeh-Schlieder theorem.},
3623         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
3624         journal = {Commun. Math. Phys.},
3625         localfile = {1968 - Borchers - On the converse of the Reeh-Schlieder theorem.pdf},
3626         pages = {269--273},
3627         title = {{On the Converse of the Reeh-Schlieder Theorem}},
3628         volume = {10},
3629         year = {1968}
3630 }
3631 
3632 @article{BorchersPohlmeyer:1968,
3633         abstract = {If for a relativistic field theory the expectation values of the commutator ...},
3634         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and K. Pohlmeyer},
3635         journal = {Commun. Math. Phys.},
3636         localfile = {1968 - Borchers, Pohlmeyer - Eine scheinbare Abschw\"{a}chung der Lokalit\"{a}tsbedingung II.pdf},
3637         title = {{Eine scheinbare Abschw\"{a}chung der Lokalit\"{a}tsbedingung. II }},
3638         volume = {8},
3639         year = {1968}
3640 }
3641 
3642 @article{ManuceauVerbeure:1968,
3643         abstract = {We give a complete characterization of quasi-free states (generalized free states) of the C.C.R. algebra. We prove that the pure quasi-free states are all Fock states and that any two Pock states are related through a symplectic automorphism (Bogoliubov transformation). We make an explicit construction of these representations which correspond to primary quasi-free states.},
3644         author = {J. Manuceau and A. Verbeure},
3645         journal = {Commun. Math. Phys.},
3646         localfile = {1968 - Manuceau, Verbeure - Quasi-free states of the CCR-algebra and Bogoliubov transformations.pdf},
3647         pages = {293--302},
3648         title = {{Quasi-Free States of the C.C.R. -- Algebra and Bogoliubov Transformations* }},
3649         volume = {9},
3650         year = {1968}
3651 }
3652 
3653 @article{Steinmann:1970,
3654         abstract = {We consider the theory of a non-localizable relativistic quantum field. Non-localizability means that the field is not a tempered distribution, but increases strongly for large momenta. Local commutativity can then not be satisfied. Instead we assume the existence of Green's functions with the usual analyticity properties. We show that in such a theory the S-matrix can be defined, and its elements can be expressed in terms of the fields by the usual reduction formulae.},
3655         author = {O. Steinmann},
3656         journal = {Commun. Math. Phys.},
3657         localfile = {1970 - Steinmann - Scattering formalism for non-localizable fields.pdf},
3658         pages = {179--194},
3659         title = {{Scattering Formalism for Non-Localizable Fields}},
3660         volume = {18},
3661         year = {1970}
3662 }
3663 
3664 @article{GlimmJaffe:1971,
3665         abstract = {We give a new proof that the locally correct Hamiltonian H(g) is self adjoint, and that the vacuum energy E(g) = infspectrum... satisfies ..., where ... and D = diam. supp.g.},
3666         author = {J. Glimm and A. Jaffe},
3667         journal = {Commun. Math. Phys.},
3668         localfile = {1971 - Glimm, Jaffe - Positivity and self adjointness of the P(phi)_2 Hamiltonian.pdf},
3669         pages = {253--258},
3670         title = {{Positivity and Self Adjointness of the P(φ)2 Hamiltonian }},
3671         volume = {22},
3672         year = {1971}
3673 }
3674 
3675 @article{OsterwalderSchrader:1973,
3676         abstract = {We establish necessary and sufficient conditions for Euclidean Green's functions to define a unique Wightman field theory.},
3677         author = {K. Osterwalder and R. Schrader},
3678         journal = {Commun. Math. Phys.},
3679         keywords = {kw:NC-Wick},
3680         localfile = {1973 - Osterwalder, Schrader - Axioms for Euclidean Green's functions.pdf},
3681         pages = {83--112},
3682         title = {{Axioms for Euclidean Green's Functions}},
3683         volume = {31},
3684         x-color = {#19ffd1},
3685         year = {1973}
3686 }
3687 
3688 @article{Woronowicz:1973,
3689         abstract = {The investigation of purifications of factor states has been carried on. It is shown, that any factor state ω of a C*-algebra admits at most one purification ώ, so one can introduce the purification map φ : φ(ω) = ώ. It turns out, that the Powers and St0rmer inequality is valid in this general situation.},
3690         author = {S. L. Woronowicz},
3691         journal = {Commun. Math. Phys.},
3692         localfile = {1973 - Woronowicz - On the Purification Map.pdf},
3693         pages = {55--67},
3694         title = {{On the Purification Map}},
3695         volume = {30},
3696         year = {1973}
3697 }
3698 
3699 @article{Buchholz:1974,
3700         abstract = {We establish a one-to-one correspondence between the continuity properties of the S-matrix at the 2-particle threshold and the rate of convergence of the Haag-Ruelle approximations Ψ(t) for asymptotic 2-particle states Ψ with smooth wavefunctions. It turns out that the norm distance ||Ψ ----------------------------------------------------------------------------- Ψ(t)|| approaches 0 like ...5/4 if the S-matrix has the normal threshold singularities and like ...3/4 in the exceptional case where the threshold has ''absorbed`` a bound state. These connections are valid both in relativistic quantum field theory and in non-relativistic models with short range interaction.},
3701         author = {D. Buchholz},
3702         journal = {Commun. Math. Phys.},
3703         localfile = {1974 - Buchholz - Threshold singularities of the S-matrix and convergence of Haag-Ruelle approximations.pdf},
3704         pages = {221--241},
3705         title = {{Threshold Singularities of the S-Matrix and Convergence of Haag-Ruelle Approximations }},
3706         volume = {39},
3707         year = {1974}
3708 }
3709 
3710 @article{Connes:1974,
3711         author = {A. Connes},
3712         journal = {Annales de l'Institut Fourier},
3713         localfile = {1974 - Connes - Caract\'{e}risation des espaces vectoriels ordonn\'{e}s sous-jacents aux alg\`{e}bres de von Neumann.pdf},
3714         pages = {121--155},
3715         title = {{Caract\'{e}risation des espaces vectoriels ordonn\'{e}s sous-jacents aux algebres de von Neumann}},
3716         volume = {24},
3717         year = {1974}
3718 }
3719 
3720 @article{Buchholz:1975,
3721         abstract = {Within the framework of local relativistic quantum theory in two space-time dimensions, we develop a collision theory for waves (the set of vectors corresponding to the eigenvalue zero of the mass operator). Since among these vectors there need not be one-particle states, the asymptotic Hilbert spaces do not in general have Fock structure. However, the definition and ``physical interpretation'' of an S-matrix is still possible. We show that this S-matrix is trivial if the correlations between localized operators vanish at large timelike distances.},
3722         author = {D. Buchholz},
3723         journal = {Commun. Math. Phys.},
3724         localfile = {1975 - Buchholz - Collision theory for waves in two dimensions and a characterization of models with trivial S-matrix.pdf},
3725         pages = {1--8},
3726         title = {{Collision Theory for Waves in Two Dimensions and a Characterization of Models with Trivial S-Matrix}},
3727         volume = {45},
3728         year = {1975}
3729 }
3730 
3731 @article{Frhlich:1975,
3732         author = {J. Fr{\"{o}}hlich},
3733         journal = {Phys. Rev. Lett.},
3734         localfile = {1975 - Fr\"{o}hlich - Quantized Sine-Gordon Equation with a Nonvanishing Mass Term in Two Space-Time Dimensions.pdf},
3735         number = {13},
3736         pages = {833--836},
3737         title = {{Quantized ``Sine-Gordon'' Equation with a Non-Vanishing Mass Term in Two Space-Time Dimensions}},
3738         volume = {34},
3739         year = {1975}
3740 }
3741 
3742 @article{Mandelstam:1975,
3743         author = {S. Mandelstam},
3744         journal = {Phys. Rev. D},
3745         localfile = {1975 - Mandelstam - Soliton operators for the quantized sine-Gordon equation.pdf},
3746         number = {10},
3747         pages = {3026--3030},
3748         title = {{Soliton operators for the quantized sine-Gordon equation}},
3749         volume = {11},
3750         year = {1975}
3751 }
3752 
3753 @article{BrosBuchholzGlaser:1976,
3754         abstract = {We analyze the space integrals Q= §d3xρ(x) of finitely localized densities ρ. It turns out that the time translated operators Q(t) are polynomials in t if Q annihilates the vacuum. In particular, Q(t) = Q in models with short- range forces and complete particle interpretation. These results are valid in the Haag-Araki framework of field theory as well as in the Wightman formalism. Lorentz covariance is not needed in the proofs.},
3755         author = {J. Bros and D. Buchholz and V. Glaser},
3756         journal = {Commun. Math. Phys.},
3757         localfile = {1976 - Bros, Buchholz, Glaser - Constants of motion in local field theory (Coleman's theorem revisited).pdf},
3758         pages = {11--22},
3759         title = {{Constants of Motion in Local Field Theory (Coleman's Theorem Revisited) }},
3760         volume = {50},
3761         year = {1976}
3762 }
3763 
3764 @article{DimockEckmann:1976,
3765         abstract = {We consider the λ(φ6-φ4) quantum field theory in two space-time dimensions. Using the Bethe-Salpeter equation, we show that there is a unique two particle bound state if the coupling constant λ>0 is sufficiently small. If m is the mass of single particles then the bound state mass is given by (...)},
3766         author = {J. Dimock and {{{{{{{{{{{{{{{{{{{{{{{{{J.-P.}}}}}}}}}}}}}}}}}}}}}}}}} Eckmann},
3767         journal = {Commun. Math. Phys.},
3768         localfile = {1976 - Dimock, Eckmann - On the bound state in weakly coupled lambda(phi6-ph4)_2.pdf},
3769         pages = {41--54},
3770         title = {{On the Bound State in Weakly Coupled λ(φ -----------------------------------------------------------------------------φ )2 }},
3771         volume = {51},
3772         year = {1976}
3773 }
3774 
3775 @article{Frhlich:1976,
3776         abstract = {A rigorous construction of new super-selection sectors ----------------------------------------------------------------------------- so-called ``soliton-sectors'' - for the quantum ``sine-Gordon'' equation and the (φ φ)2- quantum field models with explicitly broken isospin symmetry in two space- time dimensions is presented. These sectors are eigenspaces of the charge Q = §dx(gγ\&dφ)(x) with non-zero eigenvalue. The scattering theory for quantum solitons is briefly discussed and shown to have consequences for the physics in the vacuum sector. A general theory is developed which explains why soliton-sectors may exist for theories in two but not in four space-time dimensions except possibly for non-abelian Yang-Mills theories.},
3777         author = {J. Fr{\"{o}}hlich},
3778         journal = {Commun. Math. Phys.},
3779         localfile = {1976 - Fr\"{o}hlich - New super-selection sectors (``soliton-states'') in two dimensional Bose quantum field models.pdf},
3780         pages = {269--310},
3781         title = {{New Super-Selection Sectors (``Soliton-States'') in Two Dimensional Bose Quantum Field Models }},
3782         volume = {47},
3783         year = {1976}
3784 }
3785 
3786 @article{PerezWilde:1977,
3787         author = {J. F. Perez and I. F. Wilde},
3788         journal = {Phys. Rev. D},
3789         localfile = {1977 - Perez, Wilde - Localization and causality in relativistic quantum mechanics.pdf},
3790         number = {2},
3791         pages = {315--317},
3792         title = {{Localization and Causality in Relativistic Quantum Mechanics}},
3793         volume = {16},
3794         year = {1977}
3795 }
3796 
3797 @article{BergKarowskiWeisz:1979,
3798         author = {B. Berg and M. Karowski and P. Weisz},
3799         journal = {Phys. Rev. D},
3800         localfile = {1979 - Berg, Karowski, Weisz - Construction of Green's functions from an exact S matrix.pdf},
3801         number = {8},
3802         pages = {2477--2479},
3803         title = {{Construction of Green's Functions from an Exact S-Matrix}},
3804         volume = {19},
3805         year = {1979}
3806 }
3807 
3808 @article{Lcke:1979,
3809         abstract = {It is shown how classical results of axiomatic field theory such as the PCT and spin-statistics theorem may be generalized to nonlocal tempered fields. The method is also applicable to the theory of essentially local non-localizable fields.},
3810         author = {W. L{\"{u}}cke},
3811         journal = {Commun. Math. Phys.},
3812         localfile = {1979 - L\"{u}cke - PCT, Spin and Statistics, and All That for Nonlocal Wightman Fields.pdf},
3813         pages = {77--82},
3814         title = {{PCT, Spin and Statistics, and All That for Nonlocal Wightman Fields }},
3815         volume = {65},
3816         year = {1979}
3817 }
3818 
3819 @article{BorchersGarber:1980,
3820         abstract = {We develop a theory of solutions n for the Euclidean nonlinear 0(2/c+l)σ-model for arbitrary k and for a region GclR 2 . We consider a subclass of solutions characterized by a condition which is fulfilled, for G = IR2, by those n that live on the Riemann sphere §2 DlR2. We are able to characterize this class completely in terms of fe meromorphic functions, and we give an explicit inductive procedure which allows us to calculate all 0(2/c+ 1) solutions from the trivial 0(1) solutions.},
3821         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and W. D. Garber},
3822         journal = {Commun. Math. Phys.},
3823         localfile = {1980 - Borchers, Garber - Local theory of solutions for the O(2k+1) sigma-model.pdf},
3824         pages = {77--102},
3825         title = {{Local Theory of Solutions for the 0(2/c + l) σ-Model}},
3826         volume = {72},
3827         year = {1980}
3828 }
3829 
3830 @article{BorchersGarber:1980-1,
3831         abstract = {We consider continuous weak solutions of the Euler-Lagrange equations associated with the Euclidean ^-dimensional 0(N) nonlinear σ-model. We show for arbitrary N and arbitrary d that such solutions with locally square integrable gradient are real analytic.},
3832         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and W. D. Garber},
3833         journal = {Commun. Math. Phys.},
3834         localfile = {1980 - Borchers, Garber - Analyticity of solutions of the O(N) nonlinear sigma-model.pdf},
3835         pages = {299--309},
3836         title = {{Analyticity of Solutions of the O(N) Nonlinear σ-Model }},
3837         volume = {71},
3838         year = {1980}
3839 }
3840 
3841 @article{Dimock:1980,
3842         abstract = {We propose a generalization of the Haag-Kastler axioms for local observables to Lorentzian manifolds. The framework is intended to resolve ambiguities in the construction of quantum field theories on manifolds. As an example we study linear scalar fields for globally hyperbolic manifolds.},
3843         author = {J. Dimock},
3844         journal = {Commun. Math. Phys.},
3845         localfile = {1980 - Dimock - Algebras of local observables on a manifold.pdf},
3846         pages = {219--228},
3847         title = {{Algebras of Local Observables on a Manifold}},
3848         volume = {77},
3849         year = {1980}
3850 }
3851 
3852 @article{BuchholzFredenhagen:1982,
3853         abstract = {Starting from the principle of locality of observables we derive localization properties of massive particle states which hold in all models of relativistic quantum theory, including gauge theories. It turns out that particles may always be regarded as well localized distributions of matter, although their mathematical description might require the introduction of non-local (un- observable) fields, which are assigned to infinite string-like regions. In spite of the non-locality of these fields one can show that such particles obey Bose- or Fermi (para) statistics, that to each particle there exists an antiparticle and that collision states of particles exist. A selfcontained exposition of the under- lying physical ideas is given in the Introduction, and some perspectives for the structure of field-theoretic models arising from our analysis are discussed in the Conclusions.},
3854         author = {D. Buchholz and K. Fredenhagen},
3855         journal = {Commun. Math. Phys.},
3856         localfile = {1982 - Buchholz, Fredenhagen - Locality and the structure of particle states.pdf},
3857         pages = {1},
3858         slaccitation = {\%\%CITATION = CMPHA,84,1\\;\%\%},
3859         title = {{Locality and the Structure of Particle States}},
3860         volume = {84},
3861         year = {1982}
3862 }
3863 
3864 @article{Borchers:1983,
3865         abstract = {Let (A, G, α) be a C*-dynamical system with G a topological group. Let π be a representation of A. We will show that there exists a quasi- equivalent representation π to π which is a covariant representation, if and only if the folium of π is invariant under the action of G and this action is strongly continuous.},
3866         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
3867         journal = {Commun. Math. Phys.},
3868         localfile = {1983 - Borchers - C-star-algebras and automorphism groups.pdf},
3869         pages = {95--103},
3870         title = {{C*-Algebras and Automorphism Groups}},
3871         volume = {88},
3872         year = {1983}
3873 }
3874 
3875 @article{DriesslerSummers:1983,
3876         abstract = {It is shown that in a relativistic quantum field theory satisfying Wightman's axioms, there are no nontrivial field-like operators, or even bilinear forms, associated to a two (or less)-dimensional spacelike plane in Minkowski space. This generalizes Wightman's result that fields can not be defined as operators at a point and stands in contrast to Borchers' result that field operators can be associated with one-dimensional timelike planes.},
3877         author = {W. Driessler and S. J. Summers},
3878         journal = {Commun. Math. Phys.},
3879         localfile = {1983 - Driessler, Summers - Nonexistence of quantum fields associated with two-dimensional spacelike planes.pdf},
3880         pages = {221--226},
3881         slaccitation = {\%\%CITATION = CMPHA,89,221\\;\%\%},
3882         title = {{NONEXISTENCE OF QUANTUM FIELDS ASSOCIATED WITH TWO- DIMENSIONAL SPACE - LIKE PLANES}},
3883         volume = {89},
3884         year = {1983}
3885 }
3886 
3887 @article{DoplicherLongo:1984,
3888         abstract = {Contents 0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 1. Basic definitions and preliminary results . . . . . . . . . . . . . . . . . . . . . . 496 2. The functorial choice of the intermediate type l factor N A . . . . . . . . . . . . . . . 499 3. Topological and multiplicity properties of AUT(A) . . . . . . . . . . . . . . . . . . 502 4. Characterizations of Na and correspondence with automorphism groups . . . . . . . . 504 5. The local implementation of Aut(A) . . . . . . . . . . . . . . . . . . . . . . . . 512 6. The structure of the set of standard vectors . . . . . . . . . . . . . . . . . . . . . 513 7. Pseudonormal W*-inclusions, the normalcy problem . . . . . . . . . . . . . . . . . 514 8. Remarks on one-parameter interpolations of yon Neumann algebras . . . . . . . . . . 518 9. Infinite tensor products, crossed products and fixed point W*-inclusions . . . . . . . . 520 10, Applications and examples in quantum field theory . . . . . . . . . . . . . . . . . 527 11. Concluding remarks and open problems . . . . . . . . . . . . . . . . . . . . . . 532 12. Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533},
3889         author = {S. Doplicher and R. Longo},
3890         journal = {Invent. Math.},
3891         localfile = {1984 - Doplicher, Longo - Standard and split inclusions of von Neumann algebras.pdf},
3892         pages = {493--536},
3893         title = {{Standard and split inclusions of von Neumann algebras}},
3894         volume = {75},
3895         year = {1984}
3896 }
3897 
3898 @article{Longo:1984,
3899         author = {R. Longo},
3900         journal = {Invent. Math.},
3901         localfile = {1984 - Longo - Solution of the Factorial Stone-Weierstrass conjecture.pdf},
3902         pages = {145--155},
3903         title = {{Solution of the factorial Stone-Weierstra{\ss} conjecture. An application of the theory of standard split W*-inclusions.}},
3904         volume = {76},
3905         year = {1984}
3906 }
3907 
3908 @article{Woronowicz:1985,
3909         abstract = {A necessary and sufficient condition for the existence of K M S states is formulated in terms of a certam left ideal m the algebra A ~ 1 7 4},
3910         author = {S. L. Woronowicz},
3911         journal = {Lett. Math. Phys.},
3912         localfile = {1985 - Woronowicz - On the Existence of KMS states.pdf},
3913         pages = {29--31},
3914         title = {{On the Existence of KMS States}},
3915         volume = {10},
3916         year = {1985}
3917 }
3918 
3919 @article{BuchholzWichmann:1986,
3920         abstract = {Within the general framework of local quantum field theory a physically motivated condition on the energy-level density of well-localized states is proposed and discussed. It is shown that any model satisfying this condition obeys a strong form of the principle of causal (statistical) independence, which manifests itself in a specific algebraic structure of the local algebras (``split property''). It is also shown that the proposed condition holds in a free field theory.},
3921         author = {D. Buchholz and E. H. Wichmann},
3922         journal = {Commun. Math. Phys.},
3923         localfile = {1986 - Buchholz, Wichmann - Causal independence and the energy-level density of states in local quantum field theory.pdf},
3924         pages = {321},
3925         slaccitation = {\%\%CITATION = CMPHA,106,321\\;\%\%},
3926         title = {{CAUSAL INDEPENDENCE AND THE ENERGY LEVEL DENSITY OF STATES IN LOCAL QUANTUM FIELD THEORY}},
3927         volume = {106},
3928         year = {1986}
3929 }
3930 
3931 @article{DAntoniDoplicherLongoFredenhagen:1987,
3932         abstract = {The local generators of symmetry transformations which have recently been constructed from a quantum field theoretical version of Noether's theorem are shown to converge to the global ones as the volume tends to the whole space. The proof relies on the continuous volume dependence of the universal localizing maps which are associated to the local split W*-inclusions.},
3933         author = {C. D'Antoni and S. Doplicher and R. Longo and K. Fredenhagen},
3934         journal = {Commun. Math. Phys.},
3935         localfile = {1987 - D'Antoni, Doplicher, Fredenhagen, Longo - Convergence of Local Charges and Continuity Properties of W-Inclusions.pdf},
3936         pages = {325},
3937         slaccitation = {\%\%CITATION = CMPHA,110,325\\;\%\%},
3938         title = {{Convergence of Local Charges and Continuity Properties of W* Inclusions}},
3939         volume = {110},
3940         year = {1987}
3941 }
3942 
3943 @article{BrosIagolnitzer:1988,
3944         abstract = {Rigorous results on poles of the 2- and 4-point functions, which yield 2-particle asymptotic completeness and give information on the presence or absence of 2-particle bound states and resonances, are presented for weakly coupled even and non-even-field theories with mass gap in space-time dimension d = 2,3 (and for related hypothetical theories in dimension 4). Methods used are more convenient and more general than those used previously (with more limited results) for P(φ)2 theories.},
3945         author = {J. Bros and D. Iagolnitzer},
3946         journal = {Commun. Math. Phys.},
3947         localfile = {1988 - Bros, Iagolnitzer - 2-particle asymptotic completeness and bound states in weakly coupled quantum field theories.pdf},
3948         pages = {331},
3949         slaccitation = {\%\%CITATION = CMPHA,119,331\\;\%\%},
3950         title = {{TWO PARTICLE ASYMPTOTIC COMPLETENESS AND BOUND STATES IN WEAKLY COUPLED QUANTUM FIELD THEORIES}},
3951         volume = {119},
3952         year = {1988}
3953 }
3954 
3955 @article{Rehren:1988,
3956         abstract = {We discuss the exchange algebra of light-cone operators as the fundamental structure of two-dimensional conformal quantum field theory. It is necessary in order to account for the locality properties of Wightman functions of conformal fields. We discuss the consistency requirements of this new type of algebra, and obtain a classification containing the well known ``minimal models''.},
3957         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
3958         journal = {Commun. Math. Phys.},
3959         localfile = {1988 - Rehren - Locality of conformal fields in two dimensions - exchange algebra on the light-cone.pdf},
3960         pages = {675},
3961         slaccitation = {\%\%CITATION = CMPHA,116,675\\;\%\%},
3962         title = {{LOCALITY OF CONFORMAL FIELDS IN TWO-DIMENSIONS: EXCHANGE ALGEBRA ON THE LIGHT CONE}},
3963         volume = {116},
3964         year = {1988}
3965 }
3966 
3967 @article{FredenhagenRehrenSchroer:1989,
3968         abstract = {The theory of superselection sectors is generalized to situations in which normal statistics has to be replaced by braid group statistics. The essential role of the positive Markov trace of algebraic quantum field theory for this analysis is explained, and the relation to exchange algebras is established.},
3969         author = {K. Fredenhagen and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren and B. Schroer},
3970         journal = {Commun. Math. Phys.},
3971         localfile = {1989 - Fredenhagen, Rehren, Schroer - Superselection Sectors with Braid Group Statistics and Exchange Algebras I General Theory.pdf},
3972         pages = {201},
3973         slaccitation = {\%\%CITATION = CMPHA,125,201\\;\%\%},
3974         title = {{Superselection Sectors with Braid Group Statistics and Exchange Algebras. 1. General Theory}},
3975         volume = {125},
3976         year = {1989}
3977 }
3978 
3979 @article{BorchersSen:1990,
3980         abstract = {This is the first of a planned series of investigations on the theory of ordered spaces based upon four axioms. Two of these, the order (1.1.1) and the local structure (II.5.1) axioms provide the structure of the theory, and the other two [the identification (1.1.11) and cone (1.2.7) axioms] eliminate pathologies or excessive generality. In the present paper the axioms are supplemented by the nontriviality conditions (1.1.9) and a regularity property (II.4.2). The starting point is a nonempty set M and a family of distinguished subsets, called light rays, which are totally ordered. The order axiom provides the properties of this order. Positive and negative cones at a point are defined in terms of increasing and decreasing subsets and are used to extend the total order on the light rays to a partial order over all of M. The first significant result is the polygon lemma (1.2.3) which provides an essential constructive tool. A non-topological definition is found for the interiors of the cones; it leads to a ``more homogeneous'' partial order relation on M. In Sect. II, subsets called D-sets (Def. Π.2.2), possessing certain desirable properties, are studied. The key concept of perpendicularity of light rays is isolated (Def. II.3.1) and used to derive the basic ``separation properties,'' provided that the interiors of cones are nonempty. It is shown that, in a D-set, ``good'' properties of one cone can be transported along light rays, so that the structure of a D-set is homogeneous. In particular, if one cone has nonempty interior, so have all others. However, the existence of even one cone with nonempty interior does not follow from the axioms, but has to be imposed as an additional regularity condition. The local structure axiom now states that every point lies in a regular D-set. It is proved that the family of regular D-sets is closed under finite intersections. The order topology is defined as the topology which has this family as a base. This topology is Hausdorlf, and coincides with the usual topology for Minkowski spaces.},
3981         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and R. N. Sen},
3982         journal = {Commun. Math. Phys.},
3983         localfile = {1990 - Borchers, Sen - Theory of ordered spaces.pdf},
3984         pages = {593--611},
3985         title = {{Theory of Ordered Spaces}},
3986         volume = {132},
3987         year = {1990}
3988 }
3989 
3990 @article{Buchholz:1990,
3991         abstract = {The spatial Fourier transforms of local operators are analysed. It is shown that the Fourier components for non-zero momentum form weakly square integrable functions in all states of finite energy. Moreover, there hold uniform bounds for the respective L 2 -norms. The relevance of this result is illustrated in collision theory.},
3992         author = {D. Buchholz},
3993         journal = {Commun. Math. Phys.},
3994         localfile = {1990 - Buchholz - Harmonic analysis of local operators.pdf},
3995         pages = {631--641},
3996         slaccitation = {\%\%CITATION = CMPHA,129,631\\;\%\%},
3997         title = {{Harmonic Analysis of Local Operators}},
3998         volume = {129},
3999         year = {1990}
4000 }
4001 
4002 @article{Buchholz:1990-1,
4003         author = {D. Buchholz},
4004         doi = {10.1063/1.528680},
4005         journal = {J. Math. Phys.},
4006         localfile = {1990 - Buchholz - On quantum fields that generate local algebras.pdf},
4007         pages = {1839--1846},
4008         slaccitation = {\%\%CITATION = JMAPA,31,1839\\;\%\%},
4009         title = {{On quantum fields that generate local algebras}},
4010         volume = {31},
4011         year = {1990}
4012 }
4013 
4014 @article{BabelonBernard:1992,
4015         abstract = {Using exact expressions for the Ising form factors, we give a new very simple proof that the spin-spin and disorder-disorder correlation functions are governed by the Painleve III non linear differential equation. We also show that the generating function of the correlation functions of the descendents of the spin and disorder operators is a N-soliton, N → ∞, τ -function of the sinh-Gordon hierarchy. We discuss a relation of our approach to isomonodromy deformation problems, as well as further possible generalizations.},
4016         author = {O. Babelon and D. Bernard},
4017         eprint = {hep-th/9206003},
4018         journal = {Phys. Lett.},
4019         localfile = {1992 - Babelon, Bernard - From Form Factors to Correlation Functions - The Ising Model.pdf},
4020         pages = {113--120},
4021         slaccitation = {\%\%CITATION = HEP-TH/9206003\\;\%\%},
4022         title = {{From form-factors to correlation functions: The {I}sing model}},
4023         volume = {B288},
4024         year = {1992}
4025 }
4026 
4027 @article{DimockHurd:1993,
4028         abstract = {We present a rigorous renormalization group construction of the two-dimensional massless and massive quantum sine-Gordon models in finite volume for the range 0 < β < 8π. We prove analyticity in the coupling constant ζ, which implies the convergence of perturbation theory. The field correlation functions and their generating functional are analyzed and shown to have the short distance asymptotics of the free field theory. In the massive case the bounds are uniform in volume and we also obtain uniform estimates on the long distance decay of correlations.},
4029         author = {J. Dimock and T. R. Hurd},
4030         journal = {Commun. Math. Phys.},
4031         localfile = {1993 - Dimock, Hurd - Construction of the two-dimensional sine-Gordon model for beta less than 8 pi.pdf},
4032         pages = {547--580},
4033         title = {{Construction of the two-dimensional sine-Gordon model for beta less than 8 pi}},
4034         volume = {156},
4035         year = {1993}
4036 }
4037 
4038 @article{BalogHauer:1994,
4039         abstract = {We study the general structure of Smirnov{\rq}s axioms on form factors of local operators in integrable models. We find various consistency conditions that the form factor functions have to satisfy. For the special case of the O(3) σ-model we construct simple polynomial solutions for the operators of the spin-field, current, energy-momentum tensor and topological charge density.},
4040         author = {J. Balog and T. Hauer},
4041         eprint = {hep-th/9406155},
4042         journal = {Phys. Lett.},
4043         localfile = {1994 - Balog, Hauer - Polynomial Form Factors in the O(3) nonlinear sigma-model.pdf},
4044         pages = {115--121},
4045         slaccitation = {\%\%CITATION = HEP-TH/9406155\\;\%\%},
4046         title = {{Polynomial form-factors in the O(3) nonlinear sigma model}},
4047         volume = {B337},
4048         year = {1994}
4049 }
4050 
4051 @article{Hegerfeldt:1994,
4052         author = {G. C. Hegerfeldt},
4053         journal = {Phys. Rev. Lett.},
4054         localfile = {1994 - Hegerfeldt - Causality Problems for Fermis Two Atom System.pdf},
4055         pages = {596--599},
4056         slaccitation = {\%\%CITATION = PRLTA,72,596\\;\%\%},
4057         title = {{Causality problems for Fermi's two atom system}},
4058         volume = {72},
4059         year = {1994}
4060 }
4061 
4062 @article{Maison:1968,
4063         abstract = {It is proved that in a unitary representation of the Poincare- or Galileigroup the infinitesimal translations have a spectral measure without singular continuous part.},
4064         author = {D. Maison},
4065         journal = {Commun. Math. Phys.},
4066         localfile = {1968 - Maison - Eine Bemerkung zu Clustereigenschaften.pdf},
4067         number = {1},
4068         pages = {48--51},
4069         title = {{Eine Bemerkung zu Clustereigenschaften}},
4070         url = {http://projecteuclid.org/euclid.cmp/1103840982},
4071         volume = {10},
4072         year = {1968}
4073 }
4074 
4075 @article{Dybalski:2005,
4076         abstract = {Within the framework of local quantum physics we construct a scattering theory of stable, massive particles without assuming mass gaps. This extension of the Haag-Ruelle theory is based on advances in the harmonic analysis of local operators. Our construction is restricted to theories complying with a regularity property introduced by Herbst. The paper concludes with a brief discussion of the status of this assumption.},
4077         author = {W. Dybalski},
4078         eprint = {hep-th/0412226},
4079         journal = {Lett. Math. Phys.},
4080         localfile = {2004 - Dybalski - Haag-Ruelle scattering theory in presence of massless particles.pdf},
4081         pages = {27--38},
4082         slaccitation = {\%\%CITATION = HEP-TH/0412226\\;\%\%},
4083         title = {{Haag-Ruelle scattering theory in presence of massless particles}},
4084         url = {http://arxiv.org/abs/hep-th/0412226},
4085         volume = {72},
4086         year = {2005}
4087 }
4088 
4089 @article{Schwinger:1958,
4090         author = {J. Schwinger},
4091         journal = {Proc. Nat. Acad. Sci.},
4092         localfile = {1958 - Schwinger - On the Euclidian Structure of Relativistic Field Theory.pdf},
4093         pages = {956--965},
4094         title = {{On the Euclidian Structure of Relativistic Field Theory}},
4095         url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=528674},
4096         volume = {44},
4097         year = {1958}
4098 }
4099 
4100 @article{Baumann:1975,
4101         abstract = {We show within a scalar relativistic quantum field theory that if either some even truncated rc-point-function vanishes or some multiple commutator of the field operators is a c-number then the field is necessarily a generalized free field.},
4102         author = {K. Baumann},
4103         journal = {Commun. Math. Phys.},
4104         localfile = {1975 - Baumann - When is a field theory a generalized free field.pdf},
4105         number = {3},
4106         pages = {221--223},
4107         title = {{When is a field theory a generalized free field?}},
4108         url = {http://projecteuclid.org/euclid.cmp/1103899182},
4109         volume = {43},
4110         year = {1975}
4111 }
4112 
4113 @article{BuchholzVerch:1995,
4114         abstract = {For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary spacetime manifolds and provides a framework for the systematic analysis of the short distance properties of local quantum field theories. It is shown that every theory has a (possibly non-unique) scaling limit which can be classified according to its classical or quantum nature. Dilation invariant theories are stable under the action of the renormalization group. Within this framework the problem of wedge (Bisognano-Wichmann) duality in the scaling limit is discussed and some of its physical implications are outlined.},
4115         author = {D. Buchholz and R. Verch},
4116         eprint = {hep-th/9501063},
4117         journal = {Rev. Math. Phys.},
4118         localfile = {1995 - Buchholz, Verch - Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory.pdf},
4119         pages = {1195--1240},
4120         slaccitation = {\%\%CITATION = HEP-TH/9501063\\;\%\%},
4121         title = {{Scaling algebras and renormalization group in algebraic quantum field theory}},
4122         url = {http://arxiv.org/abs/hep-th/9501063},
4123         volume = {7},
4124         year = {1995}
4125 }
4126 
4127 @article{BuchholzVerch:1998,
4128         abstract = {The concept of scaling algebra provides a novel framework for the general structural analysis and classification of the short distance properties of algebras of local observables in relativistic quantum field theory. In the present article this method is applied to the simple example of massive free field theory in s = 1,2 and 3 spatial dimensions. Not quite unexpectedly, one obtains for s = 2,3 in the scaling (short distance) limit the algebra of local observables in massless free field theory. The case s =1 offers, however, some surprises. There the algebra of observables acquires in the scaling limit a non-trivial center and describes charged physical states satisfying Gauss' law. The latter result is of relevance for the interpretation of the Schwinger model at short distances and illustrates the conceptual and computational virtues of the method.},
4129         author = {D. Buchholz and R. Verch},
4130         eprint = {hep-th/9708095},
4131         journal = {Rev. Math. Phys.},
4132         localfile = {1997 - Buchholz, Verch - Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory. II. Instructive Examples.pdf},
4133         pages = {775--800},
4134         slaccitation = {\%\%CITATION = HEP-TH/9708095\\;\%\%},
4135         title = {{Scaling algebras and renormalization group in algebraic quantum field theory. II: Instructive examples}},
4136         url = {http://arxiv.org/abs/hep-th/9708095},
4137         volume = {10},
4138         year = {1998}
4139 }
4140 
4141 @article{StrelchenkoVassilevich:2007,
4142         abstract = {We analyze renormalization and the high temperature expansion of the one-loop effective action of the space-time noncommutative \phi^4 theory by using the zeta function regularization in the imaginary time formalism (i.e., on S^1 x R^3). Interestingly enough, there are no mixed (non-planar) contributions to the counterterms as well as to the power-law high temperature asymptotics. We also study the Wick rotation and formulate assumptions under which the real and imaginary time formalisms are equivalent.},
4143         author = {A. V. Strelchenko and D. V. Vassilevich},
4144         eprint = {arXiv:0705.4294 [hep-th]},
4145         journal = {Phys. Rev.},
4146         localfile = {2007 - Strelchenko, Vassilevich - On space-time noncommutative theories at finite temperature.pdf},
4147         pages = {065014},
4148         slaccitation = {\%\%CITATION = ARXIV:0705.4294\\;\%\%},
4149         title = {{On space-time noncommutative theories at finite temperature}},
4150         url = {http://arxiv.org/abs/0705.4294},
4151         volume = {D76},
4152         year = {2007}
4153 }
4154 
4155 @article{ChaichianKulishTureanuZhangZhang:2007,
4156         abstract = {Within the context of the twisted Poincar\'{e} algebra, there exists no noncommutative analogue of the Minkowski space interpreted as the homogeneous space of the Poincar\'{e} group quotiented by the Lorentz group. The usual definition of commutative classical fields as sections of associated vector bundles on the homogeneous space does not generalise to the noncommutative setting, and the twisted Poincar\'{e} algebra does not act on noncommutative fields in a canonical way. We make a tentative proposal for the definition of noncommutative classical fields of any spin over the Moyal space, which has the desired representation theoretical properties. We also suggest a way to search for noncommutative Minkowski spaces suitable for studying noncommutative field theory with deformed Poincar\'{e} symmetries.},
4157         author = {M. Chaichian and P. P. Kulish and A. Tureanu and R. B. Zhang and X. Zhang},
4158         journal = {J.Math.Phys.},
4159         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); NCQFT},
4160         pages = {042302},
4161         pdf = {http://arxiv.org/pdf/0711.0371},
4162         title = {{Noncommutative fields and actions of twisted Poincare algebra}},
4163         url = {http://arxiv.org/abs/0711.0371},
4164         v1descr = {Fri, 2 Nov 2007 18:34:47 GMT (19kb)},
4165         volume = {49},
4166         year = {2008}
4167 }
4168 
4169 @article{RiccardiSzabo:2007,
4170         abstract = {We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed properties such as the formal equivalence of Green's functions in the noncommutative and commutative theories, causality, and the absence of UV/IR mixing. We use these fields to define the functional integral formulation of twisted quantum field theory. We exploit techniques from braided tensor algebra to argue that the twisted Fock space states of these free fields obey conventional statistics. We support our claims with a detailed analysis of the modifications induced in the presence of background magnetic fields, which induces additional twists by magnetic translation operators and alters the effective noncommutative geometry seen by the twisted quantum fields. When two such field theories are dual to one another, we demonstrate that only our braided physical states are covariant under the duality.},
4171         author = {Mauro Riccardi and R. J. Szabo},
4172         journal = {JHEP},
4173         keywords = {High Energy Physics - Theory (hep-th); NCQFT},
4174         number = {HWM-07-42, EMPG-07-22},
4175         pages = {016},
4176         pdf = {http://arxiv.org/pdf/0711.1525},
4177         title = {{Duality and Braiding in Twisted Quantum Field Theory}},
4178         url = {http://arxiv.org/abs/0711.1525},
4179         v1descr = {Fri, 9 Nov 2007 19:09:24 GMT (36kb)},
4180         v1url = {http://www.arxiv.org/abs/0711.1525v1},
4181         v2descr = {Mon, 10 Dec 2007 15:46:53 GMT (36kb)},
4182         volume = {0801},
4183         year = {2008}
4184 }
4185 
4186 @article{Schroer:2007,
4187         author = {B. Schroer},
4188         journal = {Preprint},
4189         localfile = {2007 - Schroer - Localization and the interface between quantum mechanics, quantum field theory and quantum gravity.pdf},
4190         title = {{Localization and the interface between quantum mechanics, quantum field theory and quantum gravity}},
4191         url = {http://www.lqp.uni-goettingen.de/papers/07/11/07111201.html},
4192         year = {2007}
4193 }
4194 
4195 @article{Schroer:2007-2,
4196         author = {B. Schroer},
4197         journal = {Preprint},
4198         localfile = {2007 - Schroer - Constructive use of holographic projections.pdf},
4199         title = {{Constructive use of holographic projections}},
4200         url = {http://www.lqp.uni-goettingen.de/papers/07/11/07111200.html},
4201         year = {2007}
4202 }
4203 
4204 @article{Mger:1998,
4205         abstract = {We show that a large class of massive quantum field theories in 1+1 dimensions, characterized by Haag duality and the split property for wedges, does not admit locally generated superselection sectors in the sense of Doplicher, Haag and Roberts. Thereby the extension of DHR theory to 1+1 dimensions due to Fredenhagen, Rehren and Schroer is vacuous for such theories. Even charged representations which are localizable only in wedge regions are ruled out. Furthermore, Haag duality holds in all locally normal representations. These results are applied to the theory of soliton sectors. Furthermore, the extension of localized representations of a non-Haag dual net to the dual net is reconsidered. It must be emphasized that these statements do not apply to massless theories since they do not satisfy the above split property. In particular, it is known that positive energy representations of conformally invariant theories are DHR representations.},
4206         author = {M. M{\"{u}}ger},
4207         eprint = {hep-th/9705019},
4208         journal = {Rev. Math. Phys.},
4209         localfile = {1997 - M\"{u}ger - Superselection structure in massive quantum field theories in 1+1 dimensions.pdf},
4210         pages = {1147--1170},
4211         slaccitation = {\%\%CITATION = HEP-TH/9705019\\;\%\%},
4212         title = {{Superselection structure of massive quantum field theories in 1+1 dimensions}},
4213         url = {http://arxiv.org/abs/hep-th/9705019},
4214         volume = {10},
4215         year = {1998}
4216 }
4217 
4218 @book{Schmdgen:1990,
4219         address = {Basel, Boston, Berlin},
4220         author = {K. Schm{\"{u}}dgen},
4221         publisher = {Birkh\"{a}user},
4222         title = {{Unbounded Operator Algebras and Representation Theory}},
4223         year = {1990}
4224 }
4225 
4226 @article{BostelmannDAntoniMorsella:2007,
4227         abstract = {We present a method of short-distance analysis in quantum field theory that does not require choosing a renormalization prescription a priori. We set out from a local net of algebras with associated pointlike quantum fields. The net has a naturally defined scaling limit in the sense of Buchholz and Verch; we investigate the effect of this limit on the pointlike fields. Both for the fields and their operator product expansions, a well-defined limit procedure can be established. This can always be interpreted in the usual sense of multiplicative renormalization, where the renormalization factors are determined by our analysis. We also consider the limits of symmetry actions. In particular, for suitable limit states, the group of scaling transformations induces a dilation symmetry in the limit theory.},
4228         author = {H. Bostelmann and C. D'Antoni and G. Morsella},
4229         journal = {Commun. Math. Phys.},
4230         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Operator Algebras (math.OA)},
4231         number = {ESI-1985},
4232         pages = {763--798},
4233         pdf = {http://arxiv.org/pdf/0711.4237},
4234         title = {{Scaling algebras and pointlike fields: A nonperturbative approach to renormalization}},
4235         url = {http://arxiv.org/abs/0711.4237},
4236         v1descr = {Tue, 27 Nov 2007 12:10:48 GMT (44kb)},
4237         v1url = {http://www.arxiv.org/abs/0711.4237v1},
4238         v2descr = {Tue, 14 Oct 2008 09:58:40 GMT (45kb)},
4239         volume = {285},
4240         year = {2009}
4241 }
4242 
4243 @article{Abe:2007,
4244         abstract = {We present a new procedure for quantizing field theory models on a noncommutative spacetime. The new quantization depends on the noncommutative parameter explicitly and reduces to the canonical quantization in the commutative limit. It is shown that a quantum field theory constructed by the new quantization yeilds exactly the same correlation functions as those of the commutative field theory, that is, the noncommutative effects disappear completely after quantization. This implies, for instance, that by using the new quantization, the noncommutativity can be incorporated in the process of quantization, rahter than in the action as conventionally done.},
4245         author = {Y. Abe},
4246         eprint = {hep-th/0606183},
4247         journal = {Int.J.Mod.Phys.A},
4248         keywords = {High Energy Physics - Theory (hep-th)},
4249         localfile = {2007 - Abe - Noncommutative quantization for noncommutative field theory.pdf},
4250         number = {KEK-TH-1092},
4251         pages = {1181--1200},
4252         pdf = {http://arxiv.org/pdf/hep-th/0606183},
4253         slaccitation = {\%\%CITATION = HEP-TH/0606183\\;\%\%},
4254         title = {{Noncommutative Quantization for Noncommutative Field Theory}},
4255         url = {http://arxiv.org/abs/hep-th/0606183},
4256         v1descr = {Tue, 20 Jun 2006 02:26:47 GMT (22kb)},
4257         v1url = {http://www.arxiv.org/abs/hep-th/0606183v1},
4258         v2descr = {Wed, 5 Jul 2006 07:45:18 GMT (20kb)},
4259         v2url = {http://www.arxiv.org/abs/hep-th/0606183v2},
4260         v3descr = {Thu, 6 Jul 2006 13:00:26 GMT (20kb)},
4261         volume = {22},
4262         year = {2007}
4263 }
4264 
4265 @article{DaszkiewiczLukierskiWoronowicz:2007,
4266         abstract = {We introduce new $\kappa$-star product describing the multiplication of quantized $\kappa$-deformed free fields. The $\kappa$-deformation of local free quantum fields originates from two sources: noncommutativity of space-time and the $\kappa$-deformation of field oscillators algebra - we relate these two deformations. We demonstrate that for suitable choice of $\kappa$-deformed field oscillators algebra the $\kappa$-deformed version of microcausality condition is satisfied, and it leads to the deformation of the Pauli-Jordan commutation function defined by the $\kappa$-deformed mass shell. We show by constructing the $\kappa$-deformed Fock space that the use of $\kappa$-deformed oscillator algebra permits to preserve the bosonic statistics of n-particle states. The proposed star product is extended to the product of $n$ fields, which for $n=4$ defines the interaction vertex in perturbative description of noncommutative quantum $\lambda\phi^4$ field theory. It appears that the classical fourmomentum conservation law is satisfied at the interaction vertices.},
4267         author = {M. Daszkiewicz and J. Lukierski and M. Woronowicz},
4268         journal = {Phys. Rev. D},
4269         keywords = {High Energy Physics - Theory (hep-th)},
4270         pages = {105007},
4271         pdf = {http://arxiv.org/pdf/0708.1561},
4272         title = {{Towards Quantum Noncommutative $\kappa$-deformed Field Theory}},
4273         url = {http://arxiv.org/abs/0708.1561},
4274         v1descr = {Sat, 11 Aug 2007 11:47:22 GMT (14kb)},
4275         v1url = {http://www.arxiv.org/abs/0708.1561v1},
4276         v2descr = {Thu, 27 Sep 2007 14:27:14 GMT (15kb)},
4277         v2url = {http://www.arxiv.org/abs/0708.1561v2},
4278         v3descr = {Wed, 26 Mar 2008 18:57:44 GMT (16kb)},
4279         volume = {77},
4280         year = {2008}
4281 }
4282 
4283 @article{GrosseWohlgenannt:2006,
4284         abstract = {We examine the UV/IR mixing property on a $\kappa$-deformed Euclidean space for a real scalar $\phi^4$ theory. All contributions to the tadpole diagram are explicitly calculated. UV/IR mixing is present, though in a different dressing than in the case of the canonical deformation.},
4285         author = {H. Grosse and M. Wohlgenannt},
4286         eprint = {hep-th/0507030},
4287         journal = {Nucl. Phys.},
4288         localfile = {2006 - Grosse, Wohlgenannt - On kappa-deformation and UV-IR-mixing.pdf},
4289         pages = {473--484},
4290         slaccitation = {\%\%CITATION = HEP-TH/0507030\\;\%\%},
4291         title = {{On kappa-deformation and UV/IR mixing}},
4292         url = {http://arxiv.org/abs/hep-th/0507030},
4293         volume = {B748},
4294         year = {2006}
4295 }
4296 
4297 @article{FreidelKowalskiGlikmanNowak:2007-1,
4298         abstract = {We show that free $\kappa$-Minkowski space field theory is equivalent to a relativistically invariant, non local, free field theory on Minkowski space-time. The field theory we obtain has in spectrum a relativistic mode of arbitrary mass $m$ and a Planck mass tachyon. We show that while the energy momentum for the relativistic mode is essentially the standard one, it diverges for the tachyon, so that there are no asymptotic tachyonic states in the theory. It also follows that the dispersion relation is not modified, so that, in particular, in this theory the speed of light is energy-independent.},
4299         author = {L. Freidel and J. Kowalski-Glikman and S. Nowak},
4300         eprint = {hep-th/0612170},
4301         journal = {Phys. Lett.},
4302         localfile = {2007 - Freidel, Kowalski-Glikman, Nowak - From noncommutative kappa-Minkowski to Minkowski space- time.pdf},
4303         pages = {70--75},
4304         slaccitation = {\%\%CITATION = HEP-TH/0612170\\;\%\%},
4305         title = {{From noncommutative kappa-Minkowski to Minkowski space- time}},
4306         url = {http://arxiv.org/abs/hep-th/0612170},
4307         volume = {B648},
4308         year = {2007}
4309 }
4310 
4311 @article{FreidelKowalskiGlikmanNowak:2007,
4312         abstract = {This paper is devoted to detailed investigations of free scalar field theory on $\kappa$-Minkowski space. After reviewing necessary mathematical tools we discuss in depth the Lagrangian and solutions of field equations. We analyze the spacetime symmetries of the model and construct the conserved charges associated with translational and Lorentz symmetry. We show that the version of the theory usually studied breaks Lorentz invariance in a subtle way: There is an additional trans-Planckian mode present, and an associated conserved charge (the number of such modes) is not a Lorentz scalar.},
4313         author = {L. Freidel and J. Kowalski-Glikman and S. Nowak},
4314         journal = {Int.J.Mod.Phys.A},
4315         keywords = {High Energy Physics - Theory (hep-th)},
4316         pages = {2687--2718},
4317         pdf = {http://arxiv.org/pdf/0706.3658},
4318         title = {{Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry}},
4319         url = {http://arxiv.org/abs/0706.3658},
4320         v1descr = {Mon, 25 Jun 2007 14:39:17 GMT (119kb,D)},
4321         v1url = {http://www.arxiv.org/abs/0706.3658v1},
4322         v2descr = {Thu, 26 Jul 2007 09:46:25 GMT (119kb,D)},
4323         volume = {23},
4324         year = {2008}
4325 }
4326 
4327 @phdthesis{Bahns:2003,
4328         author = {D. Bahns},
4329         keywords = {NCQFT},
4330         localfile = {2003 - Bahns - Perturbative Methods on the Noncommutative Minkowski space.pdf},
4331         school = {University of Hamburg},
4332         title = {{Perturbative Methods on the Noncommutative Minkowski Space}},
4333         url = {http://www-library.desy.de/cgi-bin/showprep.pl?thesis04-004},
4334         year = {2003}
4335 }
4336 
4337 @article{ChaichianMnatsakanovaTureanuVernov:2006,
4338         abstract = {Classical results of the axiomatic quantum field theory - Reeh and Schlieder's theorems, irreducibility of the set of field operators and generalized Haag's theorem are proven in SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory. In SO(1,3) invariant theory new consequences of generalized Haag's theorem are obtained. It has been proven that the equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and thus the total cross-sections in these theories.},
4339         author = {M. Chaichian and M. N. Mnatsakanova and A. Tureanu and Yu. Vernov},
4340         eprint = {hep-th/0612112},
4341         keywords = {NCQFT},
4342         localfile = {2006 - Chaichian, Mnatsakanova, Tureanu, Vernov - Classical Theorems in Noncommutative Quantum Field Theory.pdf},
4343         slaccitation = {\%\%CITATION = HEP-TH/0612112\\;\%\%},
4344         title = {{Classical theorems in noncommutative quantum field theory}},
4345         url = {http://arxiv.org/abs/hep-th/0612112},
4346         year = {2006}
4347 }
4348 
4349 @article{ChaichianMnatsakanovaTureanuVernov:2006-1,
4350         abstract = {One of the most important results of the axiomatic quantum field theory - generalized Haag's theorem - is proven in SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory. In SO(1,3) invariant theory new consequences of generalized Haag's theorem are obtained: it has been proved that equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and total cross-sections in these theories.},
4351         author = {M. Chaichian and M. N. Mnatsakanova and A. Tureanu and Yu. Vernov},
4352         eprint = {hep-th/0611097},
4353         keywords = {NCQFT},
4354         localfile = {2006 - Chaichian, Mnatsakanova, Tureanu - Generalized Haag's theorem in SO(1,1) and SO(1,3) invariant quantum field theory.pdf},
4355         slaccitation = {\%\%CITATION = HEP-TH/0611097\\;\%\%},
4356         title = {{Generalized Haag's theorem in SO(1,1) and SO(1,3) invariant quantum field theory}},
4357         url = {http://arxiv.org/abs/hep-th/0611097},
4358         year = {2006}
4359 }
4360 
4361 @article{BalachandranPinzulQureshiVaidya:2007-1,
4362         author = {A. P. Balachandran and A. Pinzul and B. A. Qureshi and S. Vaidya},
4363         eprint = {arXiv:0708.0069 [hep-th]},
4364         journal = {Phys. Rev.},
4365         keywords = {NCQFT},
4366         localfile = {2007 - Balachandran, Pinzul, Qureshi - Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane.pdf},
4367         pages = {105025},
4368         slaccitation = {\%\%CITATION = ARXIV:0708.0069\\;\%\%},
4369         title = {{Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane}},
4370         url = {http://arxiv.org/abs/0708.0069},
4371         volume = {D76},
4372         year = {2007}
4373 }
4374 
4375 @article{BuchholzOjimaRoos:2002,
4376         abstract = {Within the framework of relativistic quantum field theory, a novel method is established which allows to distinguish non-equilibrium states admitting locally a thermodynamic interpretation. The basic idea is to compare these states with global equilibrium states (KMS states) by means of local thermal observables. With the help of such observables, the states can be ordered into classes of increasing local thermal stability. Moreover, it is possible to identify states exhibiting certain specific thermal properties of interest, such as a definite local temperature or entropy density. The method is illustrated in a simple model describing the spatio-temporal evolution of a ``big heat bang''.},
4377         author = {D. Buchholz and I. Ojima and H. Roos},
4378         eprint = {hep-ph/0105051},
4379         journal = {Annals Phys.},
4380         localfile = {2002 - Buchholz, Ojima, Roos - Thermodynamic properties of non-equilibrium states in quantum field theory.pdf},
4381         pages = {219--242},
4382         slaccitation = {\%\%CITATION = HEP-PH/0105051\\;\%\%},
4383         title = {{Thermodynamic properties of non-equilibrium states in quantum field theory}},
4384         url = {http://arxiv.org/abs/hep-ph/0105051},
4385         volume = {297},
4386         year = {2002}
4387 }
4388 
4389 @article{Buchholz:2003,
4390         abstract = {A recently proposed method for the characterization and analysis of local equilibrium states in relativistic quantum field theory is applied to a simple model. Within this model states are identified which are locally (but not globally) in thermal equilibrium and it is shown that their local thermal properties evolve according to macroscopic equations. The largest space-time regions in which local equilibrium states can exist are timelike cones. Thus, although the model does not describe dissipative effects, such states fix in a natural manner a time direction. Moreover, generically they determine a distinguished space-time point where a singularity in the temperature (a hot bang) must have occurred if local equilibrium prevailed thereafter. The results illustrate how the breaking of the time reflection symmetry at macroscopic scales manifests itself in a microscopic setting.},
4391         author = {D. Buchholz},
4392         eprint = {hep-th/0301115},
4393         journal = {Commun. Math. Phys.},
4394         localfile = {2003 - Buchholz - On hot bangs and the arrow of time in relativistic quantum field theory.pdf},
4395         pages = {271--288},
4396         slaccitation = {\%\%CITATION = HEP-TH/0301115\\;\%\%},
4397         title = {{On hot bangs and the arrow of time in relativistic quantum field theory}},
4398         url = {http://arxiv.org/abs/hep-th/0301115},
4399         volume = {237},
4400         year = {2003}
4401 }
4402 
4403 @article{Camassa:2006,
4404         abstract = {We consider a natural generalization of Haag duality to the case in which the observable algebra is restricted to a subset of the space-time and is not irreducible: the commutant and the causal complement have to be considered relatively to the ambient space. We prove this relative form of Haag duality under quite general conditions for the free scalar and electromagnetic field of space dimension d\&gt;1 in the vacuum representation. Such property is interesting in view of a theory of superselection sectors for the electromagnetic field.},
4405         author = {P. Camassa},
4406         eprint = {math-ph/0607057},
4407         localfile = {2006 - Camassa - Relative Haag duality for the free field in Fock representation.pdf},
4408         slaccitation = {\%\%CITATION = MATH-PH/0607057\\;\%\%},
4409         title = {{Relative Haag duality for the free field in Fock representation}},
4410         url = {http://arxiv.org/abs/math-ph/0607057},
4411         year = {2006}
4412 }
4413 
4414 @article{LongoRehren:2007,
4415         abstract = {The relation between two-dimensional conformal quantum field theories with and without a timelike boundary is explored.},
4416         author = {R. Longo and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
4417         journal = {Commun. Math. Phys.},
4418         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Operator Algebras (math.OA)},
4419         localfile = {2007 - Longo, Rehren - How to remove the boundary.pdf},
4420         pages = {1165--1182},
4421         pdf = {http://arxiv.org/pdf/0712.2140},
4422         title = {{How to remove the boundary in CFT - an operator algebraic procedure}},
4423         url = {http://arxiv.org/abs/0712.2140},
4424         v1descr = {Thu, 13 Dec 2007 12:44:57 GMT (27kb)},
4425         v1url = {http://www.arxiv.org/abs/0712.2140v1},
4426         v2descr = {Tue, 15 Jan 2008 15:39:11 GMT (27kb)},
4427         volume = {285},
4428         year = {2009}
4429 }
4430 
4431 @article{Seiler:2003,
4432         abstract = {In this talk I give an overview of the work done during the last 15 years in collaboration with the late Adrian Patrascioiu. In this work we accumulated evidence against the commonly accepted view that theories with nonabelian symmetry -- either two dimensional nonlinear $\sigma$ models or four dimensional Yang-Mills theories -- have the property of asymptotic freedom (AF) usually ascribed to them.},
4433         author = {E. Seiler},
4434         eprint = {hep-th/0312015},
4435         localfile = {2003 - Seiler - The case against asymptotic freedom.pdf},
4436         slaccitation = {\%\%CITATION = HEP-TH/0312015\\;\%\%},
4437         title = {{The case against asymptotic freedom}},
4438         url = {http://arxiv.org/abs/hep-th/0312015},
4439         year = {2003}
4440 }
4441 
4442 @misc{Schroer:2007-1,
4443         abstract = {Using the conformal equivalence of translational KMS states on chiral theories with dilational KMS states obtained from restricting the vacuum state to an interval (the chiral inversion of the Unruh-effect), we have previously shown that the validity of the leading logarithmic increase of the localization entropy in the attenuation length epsilon of the vacuum-polarization cloud corresponds to the well-known volume (length in chiral setting) divergence factor in the thermodynamic limit in the heat bath setting. This is not a coincidence but rather a structural consequence of the fact that both operator algebras are of the same unique von Neumann type which is completely different from that met in quantum mechanical algebras. Together with the technique of holographic projection this leads to the universal area proportionality. The main aim in this paper is to present another derivation which is more in the spirit of recent work on entanglement entropy in condensed matter physics especially that by Cardy and collaborators. The essential ingredient is the use of the split property which already has shown its constructive power in securing the existence of models of factorizing theories.},
4444         author = {B. Schroer},
4445         keywords = {High Energy Physics - Theory (hep-th)},
4446         localfile = {2007 - Schroer - Localization-Entropy from Holography on Null-Surfaces and the Split Property.pdf},
4447         month = dec,
4448         pdf = {http://arxiv.org/pdf/0712.4403},
4449         title = {{Localization-Entropy from Holography on Null-Surfaces and the Split Property}},
4450         url = {http://arxiv.org/abs/0712.4403},
4451         v1descr = {Fri, 28 Dec 2007 20:36:11 GMT (35kb)},
4452         v1url = {http://www.arxiv.org/abs/0712.4403v1},
4453         v2descr = {Mon, 31 Dec 2007 18:06:18 GMT (37kb)},
4454         year = {2007}
4455 }
4456 
4457 @misc{FrhlichGawedzki:1993,
4458         abstract = {What is quantum geometry? This question is becoming a popular leitmotiv in theoretical physics and in mathematics. Conformal field theory may catch a glimpse of the right answer. We review global aspects of the geometry of conformal fields, such as duality and mirror symmetry, and interpret them within Connes' non-commutative geometry. Extended version of lectures given by the 2nd author at the Mathematical Quantum Theory Conference, Vancouver, Canada, August 4 to 8, 1993},
4459         author = {J. Fr{\"{o}}hlich and K. Gawedzki},
4460         keywords = {High Energy Physics - Theory (hep-th)},
4461         localfile = {1993 - Fr\"{o}hlich, Gawedzki - Conformal Field Theory and Geometry of Strings.pdf},
4462         month = oct,
4463         pdf = {http://arxiv.org/pdf/hep-th/9310187},
4464         title = {{Conformal Field Theory and Geometry of Strings}},
4465         url = {http://arxiv.org/abs/hep-th/9310187},
4466         v1descr = {Thu, 28 Oct 1993 21:16:54 GMT (not stored)},
4467         v2descr = {Sun, 31 Oct 1993 14:46:28 GMT (46kb)},
4468         year = {1993}
4469 }
4470 
4471 @article{DAntoniHollands:2006,
4472         abstract = {We show that a free Dirac quantum field on a globally hyperbolic spacetime has the following structural properties: (a) any two quasifree Hadamard states on the algebra of free Dirac fields are locally quasiequivalent; (b) the split-property holds in the representation of any quasifree Hadamard state; (c) if the underlying spacetime is static, then the nuclearity condition is satisfied, that is, the free energy associated with a finitely extended subsystem (``box'') has a linear dependence on the volume of the box and goes like $\propto T^{s+1}$ for large temperatures $T$, where $s+1$ is the number of dimensions of the spacetime.},
4473         author = {C. D'Antoni and S. Hollands},
4474         eprint = {math-ph/0106028},
4475         journal = {Commun. Math. Phys.},
4476         localfile = {2006 - D'Antoni, Hollands - Nuclearity, local quasiequivalence and split property for Dirac quantum fields in curved spacetime.pdf},
4477         pages = {133--159},
4478         slaccitation = {\%\%CITATION = MATH-PH/0106028\\;\%\%},
4479         title = {{Nuclearity, local quasiequivalence and split property for Dirac quantum fields in curved spacetime}},
4480         url = {http://arxiv.org/abs/math-ph/0106028},
4481         volume = {261},
4482         year = {2006}
4483 }
4484 
4485 @article{DAntoniLongoRadulescu:2001,
4486         abstract = {We consider conformal nets on $S^1$ of von Neumann algebras, acting on the full Fock space, arising in free probability. These models are twisted local, but non-local. We extend to the non-local case the general analysis of the modular structure. The local algebras turn out to be $III_1$-factors associated with free groups. We use our set up to show examples exhibiting arbitrarily large maximal temperatures, but failing to satisfy the split property, then clarifying the relation between the latter property and the trace class conditions on $e^{-\b L}$, where $L$ is the conformal Hamiltonian.},
4487         author = {C. D'Antoni and R. Longo and F. Radulescu},
4488         eprint = {math/9810003},
4489         journal = {J. Operator Theory},
4490         localfile = {1998 - D'Antoni, Longo, Radulescu - Conformal Nets, Maximal Temperature and Models from Free Probability.pdf},
4491         pages = {195--2008},
4492         slaccitation = {\%\%CITATION = MATH/9810003\\;\%\%},
4493         title = {{Conformal Nets, Maximal Temperature and Models from Free Probability}},
4494         url = {http://arxiv.org/abs/math/9810003},
4495         volume = {45},
4496         year = {2001}
4497 }
4498 
4499 @book{Duren:1970,
4500         address = {New York},
4501         author = {P.L. Duren},
4502         localfile = {http://spaces.djvu},
4503         publisher = {Dover Publications, Inc.},
4504         series = {{Dover Books on Mathematics}},
4505         title = {{Theory of $H^p$ Spaces}},
4506         year = {1970}
4507 }
4508 
4509 @book{Conway:1995,
4510         address = {Berlin, Heidelberg, New York},
4511         author = {J.B. Conway},
4512         isbn = {0387944605},
4513         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Conway - Functions of One Complex Variable I.djvu},
4514         publisher = {Springer},
4515         title = {{Functions of one complex variable, Vol. II}},
4516         year = {1995}
4517 }
4518 
4519 @book{Boas:1954,
4520         author = {R.P. Boas},
4521         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Boas - Entire Functions.djvu},
4522         publisher = {Academic Press},
4523         title = {{Entire Functions}},
4524         year = {1954}
4525 }
4526 
4527 @article{RehrenSchroer:1987,
4528         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren and B. Schroer},
4529         journal = {Phys. Lett. B},
4530         localfile = {1987 - Rehren, Schroer - Exchange algebra on the lightcone and order-disorder 2n-point functions in the Ising field theory.pdf},
4531         pages = {84--88},
4532         title = {{Exchange algebra on the lightcone and order-disorder 2n-point functions in the Ising field theory}},
4533         volume = {198},
4534         year = {1987}
4535 }
4536 
4537 @article{SchroerTruong:1978,
4538         abstract = {We IdentIty the correct field operators which correspond to the order and disorder variables of the D = 2 Ismg model After mfmite resummatmns we obtain equality between our correlation functlons and the correlation func- tlons of McCoy, Tracy and Wu [4]},
4539         author = {B. Schroer and T.T. Truong},
4540         journal = {Phys. Lett.},
4541         localfile = {1978 - Schroer, Truong - The Relativistic Quantum Fields of the d=2 Ising Model.pdf},
4542         number = {3},
4543         pages = {371--374},
4544         title = {{The Relativistic Quantum Fields of the d=2 Ising Model}},
4545         volume = {72 B},
4546         year = {1978}
4547 }
4548 
4549 @article{SchroerTruong:1977,
4550         author = {B. Schroer and T.T. Truong},
4551         journal = {Phys. Rev. D},
4552         localfile = {1977 - Schroer, Truong - Equivilance of the Sine-Gordon and Thirring models and cumulative mass effects.pdf},
4553         number = {6},
4554         pages = {1684--1693},
4555         title = {{Equivalence of the Sine-Gordon and Thirring models and cumulative mass effects}},
4556         volume = {15},
4557         year = {1977}
4558 }
4559 
4560 @article{SchroerTruong:1979,
4561         abstract = {We show that the relict of the Kramers-Wannier duality of lattice systems in the scalin[ limit is the dual algebra and its inequivalent representation. For the Z 2 dual algebra of the lsing field theory there are precisely two inequivalent representations corresponding to T <> Tc. The T < T c representation contains a Z 2 ``spurion'' which is the remainder of a topological zero-momentum mode in the scaling limit. Our discussion of duality in the A 4 theory is less rigorous than for the lsing model.},
4562         author = {B. Schroer and T.T. Truong},
4563         journal = {Nucl. Phys. B},
4564         localfile = {1979 - Schroer, Truong - Z_2 Duality Algebra in d=2 Quantum Field Theory.pdf},
4565         pages = {125--139},
4566         title = {{Z2 Duality Algebra in d=2 Quantum Field Theory}},
4567         volume = {154},
4568         year = {1979}
4569 }
4570 
4571 @article{SchroerTruongWeisz:1979,
4572         abstract = {We construct the simplest solvable non-trivial (S ~ 1) supersymmetric model: the super- symmetric Ising field theory. The supersymmetric generalization of the duality order/dis- order algebra is discussed. Finally we attempt to ``double'' the model and comment on the connection between this doubled model and the unsolved problem of the supersymmetric sine-Gordon kink structure.},
4573         author = {B. Schroer and T.T. Truong and P. Weisz},
4574         journal = {Nucl. Phys. B},
4575         localfile = {1979 - Schroer, Truong, Weisz - Supersymmetric Ising Field Theory.pdf},
4576         pages = {140--156},
4577         title = {{Supersymmetric Ising Field Theory}},
4578         volume = {154},
4579         year = {1979}
4580 }
4581 
4582 @article{SchroerTruong:1978-1,
4583         abstract = {We show that the sin/cos functions of the axial potential of the free massive Dirac field appropriately descr~e the correlation functions of the (T > 7c) order/disorder variable of two independent superimposed Ising systems taken in the continuum limit. The well known Kramers-Wannier transformation has a simple implementation in this description. It is also demonstrated that the square relationship at the level of correlation functions between the doubled and the single versions of the Ising model originates from an operator relationship between Dirac and Majorana spinor fields in two-dimen- sional space-time. Finally a connection is made between the Wightman functions of these local field operators and the statistical correlation functions obtained by McCoy, Tracy and Wu. The use of the doubled version of the Ising model based on the Dirac field allows a simple description of the scale invariant limit and therefore bridges the gap between the rigorous work and that of Kadanoff and Ceva as well as that of Luther and Peschel.},
4584         author = {B. Schroer and T.T. Truong},
4585         journal = {Nucl. Phys. B},
4586         localfile = {1978 - Schroer, Truong - The Order-Disorder Quantum Field Operators associated with the tw-dimensional Ising Model in the Continuum Limit.pdf},
4587         pages = {80--122},
4588         title = {{The Order-Disorder Quantum Field Operators associated with the tw-dimensional Ising Model in the Continuum Limit}},
4589         volume = {144},
4590         year = {1978}
4591 }
4592 
4593 @article{SchroerTruongWeisz:1976,
4594         abstract = {We sketch a program for the explicit construction of the sine-Gordon and the massive Thirring-modelfields. This construction only works in the phase of the model in which the infinite set of ``soliton conservation laws'' are valid. The procedure entails two steps of which we only indicate explicitly the first, namely the determination of the S-matrix leading to the sine-Gordon spectrum.},
4595         author = {B. Schroer and T.T. Truong and P. Weisz},
4596         journal = {Phys. Lett.},
4597         localfile = {1976 - Schroer, Truong, Weisz - Towards an Explicit Construction of the Sine-Gordon Field Theory.pdf},
4598         pages = {422--424},
4599         title = {{Towards an Explicit Construction of the Sine-Gordon Field Theory}},
4600         volume = {63 B},
4601         year = {1976}
4602 }
4603 
4604 @article{SchroerTruongWeisz:1976-1,
4605         abstract = {We investigatethe effectsof tinite masses the short distance properties in the context on of the two-dimensional Federbush model. We comment in particular on the limiting procedure in deriving the equation of motion and on changesin Wilson expansions of certain operators as compared to the massless case.},
4606         author = {B. Schroer and T.T. Truong and P. Weisz},
4607         journal = {Ann. Phys.},
4608         localfile = {1976 - Schroer, Truong - Model Study of Nonleading Mass Singularities I.pdf},
4609         pages = {156--169},
4610         title = {{Model Study of Nonleading Mass Singularities I}},
4611         volume = {102},
4612         year = {1976}
4613 }
4614 
4615 @article{SchroerTruong:1978-2,
4616         abstract = {We show that one can take the ``square root'' of the field operator describing the disorder variable of the double D = 2 Ising model (or equivalently the XY model) recently introduced [ 11. The n-point vacuum expectation values of this new field agree in the euclidean region with the correlation functions obtained by McCoy, Tracy and Wu in the scaling limit. This ``square root operator'' written in terms of Majorana fields is identical to the operator of Sato, Miwa and Jimbo constructed by a ``Clifford rotation'' [5].},
4617         author = {B. Schroer and T.T. Truong},
4618         journal = {Phys. Lett.},
4619         localfile = {1978 - Schroer, Truong - Direct Construction of the Quantum Field Operators of the d=2 Ising Model.pdf},
4620         number = {2},
4621         pages = {149--151},
4622         title = {{Direct Construction of the Quantum Field Operators of the d=2 Ising Model}},
4623         volume = {73 B},
4624         year = {1978}
4625 }
4626 
4627 @article{Strich:2008,
4628         abstract = {The aim of this note is to present a unified approach to the results given in [BB99] and [BS04] which also covers examples of models not presented in these two papers (e.g. $d$-dimensional Minkowski space-time for $d\geq 3$). Assuming that a state is passive for an observer travelling along certain (essential) worldlines, we show that this state is invariant under the isometry group, is a KMS-state for the observer at a temperature uniquely determined by the structure constants of the Lie algebra involved and fulfills (a variant of) the Reeh-Schlieder property. Also the modular objects associated to such a state and the observable algebra of an observer are computed and a version of weak locality is examined.},
4629         author = {R. Strich},
4630         doi = {10.1063/1.2838155},
4631         journal = {J. Math. Phys.},
4632         keywords = {Mathematical Physics (math-ph)},
4633         localfile = {2008 - Strich - Passive States for Essential Observers.pdf},
4634         number = {022301},
4635         pdf = {http://arxiv.org/pdf/0801.3529},
4636         title = {{Passive States for Essential Observers}},
4637         url = {http://arxiv.org/abs/0801.3529},
4638         v1descr = {Wed, 23 Jan 2008 08:56:31 GMT (19kb)},
4639         volume = {49},
4640         year = {2008}
4641 }
4642 
4643 @article{Mund:2008,
4644         abstract = {We prove the spin-statistics theorem for massive particles obeying braid group statistics in three-dimensional Minkowski space. We start from first principles of local relativistic quantum theory. The only assumption is a gap in the mass spectrum of the corresponding charged sector, and a restriction on the degeneracy of the corresponding mass.},
4645         author = {J. Mund},
4646         journal = {Commun. Math. Phys.},
4647         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
4648         pages = {1159--1180},
4649         pdf = {http://arxiv.org/pdf/0801.3621},
4650         title = {{The Spin-Statistics Theorem for Anyons and Plektons in d=2+1}},
4651         url = {http://arxiv.org/abs/0801.3621},
4652         v1descr = {Wed, 23 Jan 2008 16:32:47 GMT (35kb)},
4653         v1url = {http://www.arxiv.org/abs/0801.3621v1},
4654         v2descr = {Fri, 18 Apr 2008 12:20:08 GMT (35kb)},
4655         volume = {286},
4656         year = {2009}
4657 }
4658 
4659 @techreport{IlievaThirring:1999,
4660         abstract = {Solutions to the Thirring model are constructed in the framework of algebraic QFT. It is shown that for all positive temperatures there are fermionic solutions only if the coupling constant is $\lambda=\sqrt{2(2n+1)\pi}, n\in {\bf N}$. These fermions are inequivalent and only for $n=1$ they are canonical fields. In the general case solutions are anyons. Different anyons (which are uncountably many) live in orthogonal spaces and obey dynamical equations (of the type of Heisenberg's ``Urgleichung'') characterized by the corresponding values of the statistic parameter. Thus statistic parameter turns out to be related to the coupling constant $\lambda$ and the whole Hilbert space becomes non-separable with a different ``Urgleichung'' satisfied in each of its sectors. This feature certainly cannot be seen by any power expansion in $\lambda$. Moreover, since the latter is tied to the statistic parameter, it is clear that such an expansion is doomed to failure and will never reveal the true structure of the theory. The correlation functions in the temperature state for the canonical dressed fermions are shown by us to coincide with the ones for bare fields, that is in agreement with the uniqueness of the $\tau$-KMS state over the CAR algebra ($\tau$ being the shift automorphism). Also the $\alpha$-anyon two-point function is evaluated and for scalar field it reproduces the result that is known from the literature.},
4661         author = {N. Ilieva and W. Thirring},
4662         journal = {Theor.Math.Phys. 121 (1999) 1294-1314; Teor.Mat.Fiz. 121 (1999) 40-65},
4663         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
4664         localfile = {1999 - Ilieva, Thirring - Anyons and the Bose-Fermi duality in the finite-temperature Thirring model.pdf},
4665         month = jun,
4666         number = {Vienna preprint UWThPh-1999-37, ESI preprint ESI-720-1999},
4667         pdf = {http://arxiv.org/pdf/math-ph/9906020},
4668         title = {{Anyons and the Bose-Fermi duality in the finite-temperature Thirring model}},
4669         url = {http://arxiv.org/abs/math-ph/9906020},
4670         v1descr = {Wed, 23 Jun 1999 14:44:45 GMT (25kb)},
4671         year = {1999}
4672 }
4673 
4674 @article{Cuntz:1977,
4675         abstract = {Abstract. We consider the C*-algebra Θn generated by n^2 isometries Sx,..., Sn on an infinite-dimensional Hubert space, with the property that SiSJ •+•... + SnS* = 1. It turns out that Θn has the structure of a crossed product of a finite simple C*-algebra J^ by a single endomorphism scaling the trace of 3F by l/n. Thus, Θn is a separable C*-algebra sharing many of the properties of a factor of type IIIλ with λ = l/n. As a consequence we show that Gn is simple and that its isomorphism type does not depend on the choice of Sl9...9Sn.},
4676         author = {J. Cuntz},
4677         journal = {Commun. Math. Phys.},
4678         localfile = {1977 - Cuntz - Simple Cstar-algebras generated by isometries.pdf},
4679         pages = {173--185},
4680         title = {{Simple C*-Algebras Generated by Isometries}},
4681         volume = {57},
4682         year = {1977}
4683 }
4684 
4685 @article{Longo:1997,
4686         abstract = {A local formula for the dimension of a superselection sector in Quantum Field Theory is obtained as vacuum expectation value of the exponential of the proper Hamiltonian. In the particular case of a chiral conformal theory, this provides a local analogue of a global formula obtained by Kac and Wakimoto within the context of representations of certain affine Lie algebras. Our formula is model independent and its version in general Quantum Field Theory applies to black hole thermodynamics. The relative free energy between two thermal equilibrium states associated with a black hole turns out to be proportional to the variation of the conditional entropy in different superselection sectors, where the conditional entropy is defined as the Connes-Stoermer entropy associated with the DHR localized endomorphism representing the sector. The constant of proportionality is half of the Hawking temperature. As a consequence the relative free energy is quantized proportionally to the logarithm of a rational number, in particular it is equal to a linear function the logarithm of an integer once the initial state or the final state is taken fixed.},
4687         author = {R. Longo},
4688         eprint = {gr-qc/9605073},
4689         journal = {Commun. Math. Phys.},
4690         pages = {451--479},
4691         slaccitation = {\%\%CITATION = GR-QC/9605073\\;\%\%},
4692         title = {{An analogue of the Kac-Wakimoto formula and black hole conditional entropy}},
4693         url = {http://arxiv.org/abs/gr-qc/9605073},
4694         volume = {186},
4695         year = {1997}
4696 }
4697 
4698 @misc{Summers:2005,
4699         abstract = {We provide an brief overview of Tomita-Takesaki modular theory and some of its applications to mathematical physics. This is an article commissioned by the Encyclopedia of Mathematical Physics, edited by J.-P. Francoise, G. Naber and T.S. Tsun, to be published by the Elsevier publishing house.},
4700         author = {S. J. Summers},
4701         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
4702         localfile = {2005 - Summers - Tomita-Takesaki Modular Theory.pdf},
4703         month = nov,
4704         pdf = {http://arxiv.org/pdf/math-ph/0511034},
4705         title = {{Tomita-Takesaki Modular Theory}},
4706         url = {http://arxiv.org/abs/math-ph/0511034},
4707         v1descr = {Wed, 9 Nov 2005 19:14:09 GMT (12kb)},
4708         year = {2005}
4709 }
4710 
4711 @article{Araki:1976,
4712         abstract = {Relative entropy of two states of a von Neumann algebra is defined in terms of the relative modular operator. The strict positivity, lower semicontinuity, convexity and monotonicity of relative entropy are proved. The Wigner-Yanase-Dyson-Lieb concavity is also proved for general von Neumann algebra.},
4713         author = {H. Araki},
4714         journal = {Publ. RIMS, Kyoto University},
4715         keywords = {Mathematical Physics (math-ph)},
4716         localfile = {1975 - Araki - Relative entropy of states of von Neumann algebras.pdf},
4717         number = {11},
4718         pages = {809--833},
4719         title = {{Relative Entropy of States of von Neumann Algebras}},
4720         year = {1976}
4721 }
4722 
4723 @article{Araki:1977,
4724         abstract = {Earlier definition of the relative entropy of two faithful normal positive linear functionals of a von Neumann algebra is generalized to non-faithful functionals. Basic properties of the relative entropy are proved for this generalization.},
4725         author = {H. Araki},
4726         journal = {Publ. RIMS, Kyoto University},
4727         keywords = {Mathematical Physics (math-ph)},
4728         localfile = {1977 - Araki - Relative entropy for states of von Neumann algebras II.pdf},
4729         number = {13},
4730         pages = {173--192},
4731         title = {{Relative Entropy of States of von Neumann Algebras II}},
4732         year = {1977}
4733 }
4734 
4735 @article{EckmannFrhlich:1974,
4736         abstract = {We consider the von Neumann algebras m) generated in the free representation by bose fields of mass m 0 with test functions supported in a bounded region ... We show that in d = 2, 3 space dimensions m) is unitarily equivalent to 0), by proving a more general theorem about equivalence of local algebras.},
4737         author = {{{{{{{{{{{{{{{{{{{{{{{{{{J.-P.}}}}}}}}}}}}}}}}}}}}}}}}} Eckmann and J. Fr{\"{o}}hlich},
4738         journal = {Annales Henri Poincare},
4739         keywords = {Mathematical Physics (math-ph)},
4740         localfile = {1974 - Eckmann, Fr\"{o}hlich - Unitary equivalence of local algebras in the quasifree representation.pdf},
4741         number = {2},
4742         pages = {201--209},
4743         title = {{Unitary equivalence of local algebras in the quasifree representation }},
4744         volume = {20},
4745         year = {1974}
4746 }
4747 
4748 @article{BuchholzSummers:1992,
4749         abstract = {An algebraic characterization of vacuum states on nets of C*-algebras over Minkowski space is given and space-time translations are reconstructed with the help of the modular structures associated with such states. The result suggests that a ``condition of geometrical modular action'' might hold in quantum field theories on a wider class of spacetime manifolds.},
4750         author = {D. Buchholz and S. J. Summers},
4751         journal = {Commun. Math. Phys.},
4752         localfile = {1993 - Buchholz, Summers - An algebraic characterization of vacuum states in Minkowski space.pdf},
4753         pages = {449--458},
4754         title = {{An Algebraic Characterization of Vacuum States in Minkowski Space }},
4755         volume = {155},
4756         year = {1992}
4757 }
4758 
4759 @article{Langmann:1994,
4760         abstract = {We discuss the restricted linear group in infinite dimensions modeled by the Schatten class of rank 2p = 4 which contains the (3 + l)-dimensional analogs of the loop groups and is closely related to Yang-Mills theory with fermions in (3 + 1)- dimensions. We give an alternative to the construction of the ``highest weight'' representation of this group found by Mickelsson and Rajeev. Our approach is close to quantum field theory, with the elements of this group regarded as Bogoliubov transformations for fermions in an external Yang-Mills field. Though these cannot be unitarily implemented in the physically relevant representation of the fermion field algebra, we argue that they can be implemented by sesquilinear forms, and that there is a (regularized) product of forms providing an appropriate group structure. On the Lie algebra level, this gives an explicit, non-perturbative construction of fermion current algebras in (3 + 1) space-time dimensions which explicitly shows that the ``wave function renormalization'' required for a consistent definition of the currents and their Lie bracket naturally leads to the Schwinger term identical with the Mickelsson-Rajeev cocycle. Though the explicit form of the Schwinger term is given only for the case p = 2, our arguments apply also to the restricted linear groups modeled by Schatten classes of rank 2p = 6,8,... corresponding to current algebras in (d + l)-dimensions, d = 5,7,},
4761         author = {E. Langmann},
4762         journal = {Commun. Math. Phys.},
4763         localfile = {1994 - Langmann - Fermion current algebras and Schwinger terms in (3+1)-dimensions.pdf},
4764         pages = {1--32},
4765         title = {{Fermion Current Algebras and Schwinger Terms in (3 + 1)-Dimensions }},
4766         volume = {162},
4767         year = {1994}
4768 }
4769 
4770 @article{LongoRehren:1995,
4771         abstract = {A subtheory of a quantum field theory specifies von Neumann subalgebras A(O) (the {\lq}observ- ables{\rq} in the space-time region O ) of the von Neumann algebras B(O) (the {\lq}fields{\rq} localized in O ). Every local algebra being a (type III1 ) factor, the inclusion A(O) in B(O) is a subfactor. The assignment of these local subfactors to the space-time regions is called a {\lq}net of subfactors{\rq}. The theory of subfactors is applied to such nets. In order to characterize the {\lq}relative position{\rq} of the subtheory, and in particular to control the restriction and induction of superselection sectors, the canonical endomorphism is studied. The crucial observation is this: the canonical endomorphism of a local subfactor extends to an endomorphism of the field net, which in turn restricts to a localized endomorphism of the observable net. The method allows to characterize, and reconstruct, local extensions B of a given theory A in terms of the observables. Various non-trivial examples are given. Several results go beyond the quantum field theoretical application.},
4772         author = {R. Longo and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
4773         journal = {Rev. Math. Phys.},
4774         keywords = {Mathematical Physics (math-ph)},
4775         localfile = {1994 - Longo, Rehren - Nets of Subfactors.pdf},
4776         pages = {567--598},
4777         title = {{Nets of Subfactors}},
4778         volume = {7},
4779         year = {1995}
4780 }
4781 
4782 @article{MundSchrader:1994,
4783         abstract = {Using the theory of fibre bundles, we provide several equivalent intrinsic descriptions for the Hilbert spaces of $n$ ``free'' nonrelativistic and relativistic plektons in two space dimensions. These spaces carry a ray representation of the Galilei group and a unitary representation of the Poincar\'{e} group respectively. In the relativistic case we also discuss the situation where the braid group is replaced by the ribbon braid group.},
4784         author = {J. Mund and R. Schrader},
4785         journal = {Preprint},
4786         keywords = {Mathematical Physics (math-ph)},
4787         localfile = {1994 - Mund, Schrader - Hilbert Spaces for Nonrelativistic and Relativistic Free Plektons (Particles with Braid Group Statistics).pdf},
4788         title = {{Hilbert Spaces for Nonrelativistic and Relativistic ``Free'' Plektons (Particles with Braid Group Statistics)}},
4789         year = {1994}
4790 }
4791 
4792 @article{Jr:1996-1,
4793         abstract = {Starting from a chiral conformal Haag-Kastler net on 2 dimensional Minkowski space we construct associated charged pointlike localized fields which intertwine between arbitrary superselection sectors with finite statistics of the theory. This amounts to a proof of the Spin-Statistics theorem, the PCT theorem and the existence of operator product expansions. This paper generalizes similar results of a recently published paper by Fredenhagen and the author \cite{FrJ} from the neutral vacuum sector to the the full theory with arbitrary charge and finite statistics.},
4794         author = {M. J{\"{o}}r{\ss}},
4795         journal = {Lett. Math. Phys.},
4796         localfile = {1995 - J\"{o}r{\ss} - The Construction of Pointlike Localized Charged Fields from Conformal Haag-Kastler Nets.pdf},
4797         pages = {257--274},
4798         title = {{The Construction of Pointlike Localized Charged Fields from Conformal Haag-Kastler Nets}},
4799         url = {http://arxiv.org/abs/hep-th/9506016},
4800         volume = {38},
4801         year = {1996}
4802 }
4803 
4804 @article{LiguoriMintchev:1995,
4805         abstract = {Fock representations for quantum fields which obey generalized statistics are explicitly constructed. The main features of these representations are investigated.},
4806         author = {A. Liguori and M. Mintchev},
4807         journal = {Lett. Math. Phys.},
4808         keywords = {Mathematical Physics (math-ph)},
4809         localfile = {1995 - Liguori, Mintchev - Fock Spaces with Generalized Statistics.pdf},
4810         pages = {283--295},
4811         title = {{Fock Spaces with Generalized Statistics}},
4812         volume = {33},
4813         year = {1995}
4814 }
4815 
4816 @article{BalogNiedermaierHauer:1996,
4817         abstract = {The two-point functions of the energy-momentum tensor and the Noether current are used to probe the O(3) nonlinear sigma model in an energy range below 10^4 in units of the mass gap $m$. We argue that the form factor approach, with the form factor series trunctated at the 6-particle level, provides an almost exact solution of the model in this energy range. The onset of the (2-loop) perturbative regime is found to occur only at energies around $100m$.},
4818         author = {J. Balog and M. R. Niedermaier and T. Hauer},
4819         journal = {Phys. Lett. B},
4820         localfile = {1996 - Balog, Niedermaier, Hauer - Perturbative versus Non-perturbative QFT Lessons from the O(3) NLS Model.pdf},
4821         pages = {224--232},
4822         title = {{Perturbative versus Non-perturbative QFT -- Lessons from the O(3) NLS Model}},
4823         url = {http://arxiv.org/abs/hep-th/9604161},
4824         volume = {386},
4825         year = {1996}
4826 }
4827 
4828 @article{Filk:1996,
4829         abstract = {We investigate field theories defined on spaces with non-commutative coordinates corresponding to deformations of flat spaces as e.g. the Euclidean plane or Minkowski space. When E-expressed in terms of ordinary complex fields, the interactions are non-local. Despite this fact, these field theories exhibit the same kind of divergencies as the non-deformed models, due to special graph-topologicalproperties of cocylcles connected with the non-commutativecoordinates.},
4830         author = {T. Filk},
4831         journal = {Phys. Lett. B},
4832         keywords = {NCQFT},
4833         localfile = {1996 - Filk - Divergenices of a field theory on quantum space.pdf},
4834         pages = {53--58},
4835         title = {{Divergencies in a field theory on quantum space}},
4836         volume = {376},
4837         year = {1996}
4838 }
4839 
4840 @article{GrosseLangmannRaschhofer:1997,
4841         abstract = {We study the Luttinger-Schwinger model, i.e. the (1+1) dimensional model of massless Dirac fermions with a non-local 4-point interaction coupled to a U(1)-gauge field. The complete solution of the model is found using the boson-fermion correspondence, and the formalism for calculating all gauge invariant Green functions is provided. We discuss the role of anomalies and show how the existence of large gauge transformations implies a fermion condensate in all physical states. The meaning of regularization and renormalization in our well-defined Hilbert space setting is discussed. We illustrate the latter by performing the limit to the Thirring-Schwinger model where the interaction becomes local.},
4842         author = {H. Grosse and E. Langmann and E. Raschhofer},
4843         journal = {Annals Phys.},
4844         localfile = {1996 - Grosse, Langmann, Raschhofer - The Luttinger--Schwinger Model.pdf},
4845         pages = {310--331},
4846         title = {{The Luttinger-Schwinger Model}},
4847         url = {http://arxiv.org/abs/hep-th/9609206},
4848         volume = {253},
4849         year = {1997}
4850 }
4851 
4852 @article{Borchers:1997-1,
4853         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
4854         journal = {Preprint},
4855         localfile = {1997 - Borchers - Half-sided Translations in Connection with Modular Groups as a Tool in Quantum Field Theory.pdf},
4856         title = {{Half--sided Translations in Connection with Modular Groups as a Tool in Quantum Field Theory }},
4857         year = {1997}
4858 }
4859 
4860 @phdthesis{Mger:1997,
4861         author = {M. M{\"{u}}ger},
4862         localfile = {1997 - M\"{u}ger - Superselection Structure of Quantum Field Theories in 1+1 Dimenions PhD.pdf},
4863         school = {Hamburg},
4864         title = {{Superselection structure of quantum field theories in 1+1 dimensions}},
4865         year = {1997}
4866 }
4867 
4868 @article{Schroer:1997,
4869         abstract = {It has been known that the Wigner representation theory for positive energy orbits permits a useful localization concept in terms of certain lattices of real subspaces of the complex Hilbert -space. This ''modular localization'' is not only useful in order to construct interaction-free nets of local algebras without using non-unique ''free field coordinates'', but also permits the study of properties of localization and braid-group statistics in low-dimensional QFT. It also sheds some light on the string-like localization properties of the 1939 Wigner's ''continuous spin'' representations.We formulate a constructive nonperturbative program to introduce interactions into such an approach based on the Tomita-Takesaki modular theory. The new aspect is the deep relation of the latter with the scattering operator.},
4870         author = {B. Schroer},
4871         journal = {Nucl. Phys. B},
4872         localfile = {1997 - Schroer - Wigner Representation Theory of the Poincare Group, Localization, Statistics and the S-Matrix.pdf},
4873         pages = {519--546},
4874         title = {{Wigner Representation Theory of the Poincare Group, Localization, Statistics and the S-Matrix}},
4875         url = {http://arxiv.org/abs/hep-th/9608092},
4876         volume = {499},
4877         year = {1997}
4878 }
4879 
4880 @phdthesis{Wulkenhaar:1997,
4881         abstract = {Starting with a Hilbert space endowed with a representation of a skew--adjoint Lie algebra and an action of a generalized Dirac operator, we develop a math- ematical concept towards gauge field theories. This concept shares common features with the non--commutative geometry a la Connes / Lott, differs from that, however, by the implementation of skew--adjoint Lie algebras instead of associative star-algebras. Taking as the Lie algebra the tensor product of the functions algebra and an appropriate matrix Lie algebra, together with phys- ically motivated representations on the fermionic Hilbert space and a combi- nation of the classical Dirac operator and fermionic mass matrices as the gen- eralized Dirac operator, we recover prominent models of particle physics, ex- tended by tree--level predictions for the masses of Higgs and gauge bosons.},
4882         author = {R. Wulkenhaar},
4883         localfile = {1997 - Wulkenhaar - Non-Associative Geometry - Unified Models Based on L-Cycles -- PhD Thesis.pdf},
4884         school = {Leipzig},
4885         title = {{Non--Associative Geometry - Unified Models Based on L--Cycles }},
4886         year = {1997}
4887 }
4888 
4889 @article{Dorey:1998,
4890         abstract = {Notes on exact S-matrices in 1+1 dimensions, based on lectures given at the 1996 Eotvos Graduate School, Budapest, and at the Institut Henri Poincare, Paris.},
4891         author = {P. Dorey},
4892         journal = {Preprint},
4893         localfile = {1998 - Dorey - Exact S-matrices.pdf},
4894         title = {{Exact S-matrices}},
4895         url = {http://arxiv.org/abs/hep-th/9810026},
4896         year = {1998}
4897 }
4898 
4899 @article{EvesonFewster:1998,
4900         abstract = {We generalise results of Ford and Roman which place lower bounds -- known as quantum inequalities -- on the renormalised energy density of a quantum field averaged against a choice of sampling function. Ford and Roman derived their results for a specific non-compactly supported sampling function; here we use a different argument to obtain quantum inequalities for a class of smooth, even and non-negative sampling functions which are either compactly supported or decay rapidly at infinity. Our results hold in $d$-dimensional Minkowski space ($d\ge 2$) for the free real scalar field of mass $m\ge 0$. We discuss various features of our bounds in 2 and 4 dimensions. In particular, for massless field theory in 2-dimensional Minkowski space, we show that our quantum inequality is weaker than Flanagan's optimal bound by a factor of 3/2.},
4901         author = {S. P. Eveson and C. J. Fewster},
4902         journal = {Phys. Rev. D},
4903         localfile = {1998 - Eveson, Fewster - Bounds on negative energy densities in flat spacetime.pdf},
4904         title = {{Bounds on negative energy densities in flat spacetime}},
4905         volume = {58},
4906         year = {1998}
4907 }
4908 
4909 @article{Schroer:1998,
4910         author = {B. Schroer},
4911         journal = {Preprint},
4912         localfile = {1998 - Schroer - Localization and Nonperturbative Local Quantum Physics.pdf},
4913         title = {{A Course On: Modular Localization and Non-Perturbative Local Quantum Physics}},
4914         year = {1998}
4915 }
4916 
4917 @article{Schroer:1999,
4918         abstract = {In this paper I continue the study of the new framework of modular localization and its constructive use in the nonperturbative d=1+1 Karowski-Weisz-Smirnov formfactor program. Particular attention is focussed on the existence of semilocal generators of the wedge-localized algebra without vauum polarization (FWG-operators) which are closely related to objects fulfilling the Zamolodchikov-Faddeev algebraic structure. They generate a ``thermal Hilbert space'' and allow to understand the equivalence of the KMS conditions with the so-called cyclicity equation for formfactors which was known to be closely related to crossing symmetry properties. The modular setting gives rise to interesting new ideas on ``free'' d=2+1 anyons and plektons.},
4919         author = {B. Schroer},
4920         journal = {Annals Phys.},
4921         localfile = {1998 - Schroer - Modular Wedge Localization and the d=1+1 Formfactor Program.pdf},
4922         pages = {190--223},
4923         title = {{Modular Wedge Localization and the d=1+1 Formfactor Program}},
4924         url = {http://arxiv.org/abs/hep-th/9712124},
4925         volume = {275},
4926         year = {1999}
4927 }
4928 
4929 @article{Wassermann:1998,
4930         abstract = {Fusion of positive energy representations is defined using Connes' tensor product for bimodules over a von Neumann algebra. Fusion is computed using the analytic theory of primary fields and explicit solutions of the Knizhnik-Zamolodchikov equation.},
4931         author = {A. Wassermann},
4932         journal = {Preprint},
4933         localfile = {1998 - Wassermann - OPERATOR ALGEBRAS AND CONFORMAL FIELD THEORY III.pdf},
4934         title = {{Operator Algebras and Conformal Field Theory III. Fusion of positive }},
4935         url = {http://arxiv.org/abs/math/9806031},
4936         year = {1998}
4937 }
4938 
4939 @phdthesis{Florig:1999,
4940         author = {M. Florig},
4941         localfile = {1999 - Florig - Geometric Modular Action -- PhD-Thesis.pdf},
4942         school = {Gainesville},
4943         title = {{Geometric Modular Action}},
4944         year = {1999}
4945 }
4946 
4947 @article{Oeckl:2001,
4948         abstract = {We develop a general framework for quantum field theory on noncommutative spaces, i.e., spaces with quantum group symmetry. We use the path integral approach to obtain expressions for $n$-point functions. Perturbation theory leads us to generalised Feynman diagrams which are braided, i.e., they have non-trivial over- and under-crossings. We demonstrate the power of our approach by applying it to $\phi^4$-theory on the quantum 2-sphere. We find that the basic divergent diagram of the theory is regularised.},
4949         author = {R. Oeckl},
4950         journal = {Commun. Math. Phys.},
4951         localfile = {1999 - Oeckl - Braided Quantum Field Theory.pdf},
4952         pages = {451--473},
4953         title = {{Braided Quantum Field Theory}},
4954         url = {http://arxiv.org/abs/hep-th/9906225},
4955         volume = {217},
4956         year = {2001}
4957 }
4958 
4959 @article{Schroer:2000,
4960         abstract = {Recent ideas on modular localization in local quantum physics are used to clarify the relation between on- and off-shell quantities in particle physics; in particular the relation between on-shell crossing symmetry and off-shell Einstein causality. Among the collateral results of this new nonperturbative approach are profound relations between crossing symmetry of particle physics and Hawking-Unruh like thermal aspects (KMS property, entropy attached to horizons) of quantum matter behind causal horizons, aspects which hitherto were exclusively related with Killing horizons in curved spacetime rather than with localization aspects in Minkowski space particle physics. The scope of this modular framework is amazingly wide and ranges from providing a conceptual basis for the d=1+1 bootstrap-formfactor program for factorizable d=1+1 models to a decomposition theory of QFT's in terms of a finite collection of unitarily equivalent chiral conformal theories placed a specified relative position within a common Hilbert space (in d=1+1 a holographic relation and in higher dimensions more like a scanning). The new framework gives a spacetime interpretation to the Zamolodchikov-Faddeev algebra and explains its thermal aspects.},
4961         author = {B. Schroer},
4962         journal = {J. Phys. A},
4963         localfile = {1999 - Schroer - New Concepts in Particle Physics from Solution of an Old Problem.pdf},
4964         pages = {5231},
4965         title = {{New Concepts in Particle Physics from Solution of an Old Problem}},
4966         url = {http://arxiv.org/abs/hep-th/9908021},
4967         volume = {33},
4968         year = {2000}
4969 }
4970 
4971 @phdthesis{Bostelmann:2000,
4972         abstract = {Bei der Formulierung von Modellen in der relativistischen Quantenphysik spielen punkt- artig lokalisierte Me{\ss}gr¨{\ss}en (Quantenfelder) eine zentrale Rolle. Sie bilden die begriffliche o Grundlage f¨r Feldgleichungen oder Wirkungsprinzipien, mit deren Hilfe sich spezielle Mo- u delle auszeichnen und st¨rungstheoretisch behandeln lassen. o Die scharfe Lokalisierung der Quantenfelder im Ortsraum f¨hrt aufgrund der quanten- u mechanischen Unsch¨rferelation jedoch zu Singularit¨ten, die eine mathematisch rigorose a a Formulierung erschweren. Insbesondere sind Produkte solcher Felder am gleichen Raum- Zeit-Punkt im allgemeinen nicht wohldefiniert, sondern weisen Divergenzen auf. Dies f¨hrt u zu Problemen etwa bei der Behandlung nichtlinearer Feldgleichungen, von denen man er- wartet, da{\ss} sie die Dynamik wechselwirkender Modelle bestimmen. Die vorliegende Arbeit stellt eine neue Methode zur modellunabh¨ngigen Analyse der a Eigenschaften von Punktfeldern vor. Ausgehend von einer Formulierung der Theorie durch Me{\ss}gr¨{\ss}en, die in endlichen Raum-Zeit-Gebieten lokalisiert sind (und damit keine Singu- o larit¨ten aufweisen), untersuchen wir deren Kurzabstandsverhalten. Wir geben ein nat¨rli- a u ches Phasenraumkriterium an, das uns erlaubt, den Feldinhalt der Theorie zu bestimmen, indem wir Punktfelder als Limiten immer besser lokalisierter Observablen konstruieren. Deren singul¨res Verhalten wird analysiert. a Dasselbe Phasenraumkriterium erm¨glicht auch die Behandlung von Produkten der o konstruierten Felder: Im Limes kleiner Abst¨nde kann eine asymptotische Reihenentwick- a lung der Feldprodukte (Operatorproduktentwicklung) etabliert werden. Diese gestattet die Untersuchung von Normalprodukten und damit die Formulierung nichtlinearer Feldglei- chungen im vorliegenden Rahmen. Das genannte modell¨bergreifende Kriterium wird beispielhaft in Modellen der freien u Feldtheorie explizit hergeleitet und untersucht; die Ergebnisse lassen Extrapolationen auch auf den wechselwirkenden Fall zu.},
4973         author = {H. Bostelmann},
4974         localfile = {2000 - Bostelmann - Lokale Algebren und Operatorprodukte am Punkt.pdf},
4975         school = {G\"{o}ttingen},
4976         title = {{Lokale Algebren und Operatorprodukte am Punkt}},
4977         year = {2000}
4978 }
4979 
4980 @misc{CareyPhillipsRennie:2008,
4981         abstract = {This paper presents, by example, an index theory appropriate to algebras without trace. Whilst we work exclusively with the Cuntz algebras the exposition is designed to indicate how to develop a general theory. Our main result is an index theorem (formulated in terms of spectral flow) using a twisted cyclic cocycle where the twisting comes from the modular automorphism group for the canonical gauge action on the Cuntz algebra. We introduce a modified $K_1$-group of the Cuntz algebra so as to pair with this twisted cocycle. As a corollary we obtain a noncommutative geometry interpretation for Araki's notion of relative entropy in this example. We also note the connection of this example to the theory of noncommutative manifolds.},
4982         author = {A. L. Carey and J. Phillips and A. Rennie},
4983         keywords = {K-Theory and Homology (math.KT); Operator Algebras (math.OA)},
4984         localfile = {2008 - Carey, Phillips, Rennie - Twisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras.pdf},
4985         month = jan,
4986         pdf = {http://arxiv.org/pdf/0801.4605},
4987         title = {{Twisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras}},
4988         url = {http://arxiv.org/abs/0801.4605},
4989         v1descr = {Wed, 30 Jan 2008 05:47:03 GMT (45kb)},
4990         year = {2008}
4991 }
4992 
4993 @misc{CareyRennieTong:2008,
4994         abstract = {In [CPR2], we presented a K-theoretic approach to finding invariants of algebras with no non-trivial traces. This paper presents a new example that is more typical of the generic situation. This is the case of an algebra that admits only non-faithful traces, namely SU\_q(2), and also KMS states. Our main results are index theorems (which calculate spectral flow), one using ordinary cyclic cohomology and the other using twisted cyclic cohomology, where the twisting comes from the generator of the modular group of the Haar state. In contrast to the Cuntz algebras studied in [CPR2], the computations are considerably more complex and interesting, because there are nontrivial `eta' contributions to this index.},
4995         author = {A. L. Carey and A. Rennie and K. Tong},
4996         keywords = {Operator Algebras (math.OA); Quantum Algebra (math.QA)},
4997         month = feb,
4998         pdf = {http://arxiv.org/pdf/0802.0317},
4999         title = {{Spectral flow invariants and twisted cyclic theory from the Haar state on SU\_q(2)}},
5000         url = {http://arxiv.org/abs/0802.0317},
5001         v1descr = {Mon, 4 Feb 2008 00:15:53 GMT (35kb)},
5002         year = {2008}
5003 }
5004 
5005 @misc{Summers:2008,
5006         abstract = {An overview is given of what mathematical physics can currently say about the vacuum state for relativistic quantum field theories on Minkowski space. Along with a review of classical results such as the Reeh--Schlieder Theorem and its immediate and controversial consequences, more recent results are discussed. These include the nature of vacuum correlations and the degree of entanglement of the vacuum, as well as the striking fact that the modular objects determined by the vacuum state and algebras of observables localized in certain regions of Minkowski space encode a remarkable range of physical information, from the dynamics and scattering behavior of the theory to the external symmetries and even the space--time itself. These modular objects also provide an intrinsic characterization of the vacuum state itself, a fact which is of particular relevance to the search for criteria to select physically significant reference states for quantum field theories on curved space--times.},
5007         author = {S. J. Summers},
5008         keywords = {Mathematical Physics (math-ph)},
5009         localfile = {2008 - Summers - Yet More Ado About Nothing: The Remarkable Relativistic Vacuum State.pdf},
5010         month = feb,
5011         pdf = {http://arxiv.org/pdf/0802.1854},
5012         title = {{Yet More Ado About Nothing: The Remarkable Relativistic Vacuum State}},
5013         url = {http://arxiv.org/abs/0802.1854},
5014         v1descr = {Wed, 13 Feb 2008 15:58:09 GMT (29kb)},
5015         year = {2008}
5016 }
5017 
5018 @misc{Schroer:2008,
5019         abstract = {Indecomposable positive energy quantum matter comes in form of 3 families: one massive and two massless families of which the so called ``infinite spin'' family is either not mentioned at all or, if it is presented for reasons of completeness, it is immediately dismissed as ``unphysical'' without pinpointing at a violated principle. Using novel methods which are particularly suited for problems of localization, it was shown that these representations cannot be generated by pointlke localized fields but rather require the introduction of spacelike semiinfinite stringlike generators. Arguing that their field algebras do not admit any compactly localizable subalgebras, we are led to a situation of purely gravitating matter which cannot be registered in any particle counter. The problems one encounters in formulating interactions with ordinary matter suggest that this third kind of positive energy matter in Wigner's classification may also be inert relative to standard matter.},
5020         author = {B. Schroer},
5021         keywords = {Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
5022         localfile = {2008 - Schroer - Is inert matter from indecomposable positive energy infinite spin representations the much sought-after dark matter.pdf},
5023         month = feb,
5024         pdf = {http://arxiv.org/pdf/0802.2098},
5025         title = {{Is inert matter from indecomposable positive energy ``infinite spin'' representations the much sought-after dark matter?}},
5026         url = {http://arxiv.org/abs/0802.2098},
5027         v1descr = {Thu, 14 Feb 2008 20:40:40 GMT (14kb)},
5028         v1url = {http://www.arxiv.org/abs/0802.2098v1},
5029         v2descr = {Fri, 15 Feb 2008 10:30:28 GMT (15kb)},
5030         year = {2008}
5031 }
5032 
5033 @article{Verch:1993,
5034         abstract = {Abstract. It is shown that the operator A^1/2, where A is any positive self-adjoint extension of a positive operator of the form ``Laplace Beltrami operator + potential'' on an n-dimensional Riemannian manifold, is strongly antilocal. Using this result, a Reeh-Schlieder theorem for the canonical vacuum of the Klein-Gordon field propagating in ultrastatic spacetimes is derived. In a further application, we gain weaker versions of the Reeh-Schlieder theorem for more general situations.},
5035         author = {R. Verch},
5036         journal = {Lett. Math. Phys.},
5037         keywords = {Mathematical Physics (math-ph); QFT on curved spacetime},
5038         localfile = {1993 - Verch - Antilocality and a Reeh-Schlieder Theorem on Manifolds.pdf},
5039         pages = {143--154},
5040         title = {{Antilocality and a Reeh-Schlieder Theorem on Manifolds}},
5041         volume = {28},
5042         year = {1993}
5043 }
5044 
5045 @misc{Summers:2008-1,
5046         abstract = {Assertions made in a document recently deposited in the arXiv are refuted.},
5047         author = {S. J. Summers},
5048         keywords = {Mathematical Physics (math-ph)},
5049         localfile = {2008 - Summers - ``On the Impossibility of a Poincare-Invariant Vacuum State with Unit Norm'' Refuted.pdf},
5050         month = feb,
5051         pdf = {http://arxiv.org/pdf/0802.2935},
5052         title = {{``On the Impossibility of a Poincare-Invariant Vacuum State with Unit Norm'' Refuted}},
5053         url = {http://arxiv.org/abs/0802.2935},
5054         v1descr = {Wed, 20 Feb 2008 20:29:54 GMT (5kb)},
5055         year = {2008}
5056 }
5057 
5058 @misc{Berkowitz:2008,
5059         abstract = {In the standard construction of Quantum Field Theory, a vacuum state is required. The vacuum is a vector in a separable, infinite-dimensional Hilbert space often referred to as Fock space. By definition the vacuum wavestate depends on nothing and must be translationally invariant. We show that any such translationally-invariant vector must have a norm that is either divergent or equal to zero. It is impossible for any state to be both everywhere translationally invariant and also have a norm of one. The axioms of QFT cannot be made internally consistent.},
5060         author = {J. Berkowitz},
5061         keywords = {Crackpot Stuff},
5062         month = feb,
5063         pdf = {http://arxiv.org/pdf/0802.0216},
5064         title = {{On the Impossibility of a Poincare-invariant Vacuum State with Unit Norm}},
5065         url = {http://arxiv.org/abs/0802.0216},
5066         v1descr = {Fri, 1 Feb 2008 22:40:04 GMT (47kb)},
5067         v1url = {http://www.arxiv.org/abs/0802.0216v1},
5068         v2descr = {Thu, 7 Feb 2008 03:19:01 GMT (47kb)},
5069         year = {2008}
5070 }
5071 
5072 @article{Longo:1989,
5073         abstract = {We identify the statistical dimension of a superselection sector in a local quantum field theory with the square root of the index of a localized endomorphism of the quasi-local C*-algebra that represents the sector. As a consequence in a two-dimensional theory the possible values of the statistical dimension below 2 are restricted to a given discrete set.},
5074         author = {R. Longo},
5075         journal = {Commun. Math. Phys.},
5076         localfile = {1989 - Longo - Index of subfactors and statistics of quantum fields I.pdf},
5077         pages = {217--247},
5078         title = {{Index of subfactors and statistics of quantum fields I}},
5079         volume = {126},
5080         year = {1989}
5081 }
5082 
5083 @article{MackSchomerus:1990,
5084         abstract = {According to the theory of superselection sectors of Doplicher, Haag, and Roberts, field operators which make transitions between different superselection sectors - i.e. different irreducible representations of the observable algebra - are to be constructed by adjoining localized endomorphisms to the algebra of local observables. We find the relevant endomorphisms of the chiral algebra of observables in the minimal conformal model with central charge c=1/2 (Ising model). We show by explicit and elementary construction how they determine a representation of the braid group B^ which is associated with a Temperley-Lieb-Jones algebra. We recover fusion rules, and compute the quantum dimensions of the superselection sectors. We exhibit a field algebra which is quantum group covariant and acts in the Hubert space of physical states. It obeys local braid relations in an appropriate weak sense.},
5085         author = {G. Mack and V. Schomerus},
5086         journal = {Commun. Math. Phys.},
5087         localfile = {1990 - Mack, Schomerus - Conformal field algebras with quantum symmetry from the theory of superselection sectors.pdf},
5088         pages = {139--196},
5089         title = {{Conformal Field Algebras with Quantum Symmetry from the Theory of Superselection Sectors }},
5090         volume = {134},
5091         year = {1990}
5092 }
5093 
5094 @article{Jaffe:2000,
5095         abstract = {We review the emergence of constructive quantum field theory, we discuss how it fits into the framework of mathematics and physics, and we point to a major unsolved question.},
5096         author = {A. Jaffe},
5097         journal = {Preprint},
5098         localfile = {2000 - Jaffe - Constructive Quantum Field Theory.pdf},
5099         title = {{Constructive Quantum Field Theory}},
5100         year = {2000}
5101 }
5102 
5103 @article{Schroer:1999-1,
5104         abstract = {The present state of QFT is analysed from a new viewpoint whose mathematical basis is the modular theory of von Neumann algebras. Its physical consequences suggest new ways of dealing with interactions, symmetries, Hawking-Unruh thermal properties and possibly also extensions of the scheme of renormalized perturbation theory. Interactions are incorporated by using the fact that the S-matrix is a relative modular invariant of the interacting- relative to the incoming net of wedge algebras. This new point of view allows many interesting comparisions with the standard quantization approach to QFT and is shown to be firmly rooted in the history of QFT. Its radical ``change of paradigm'' aspect becomes particularily visible in the quantum measurement problem.},
5105         author = {B. Schroer},
5106         journal = {Preprint},
5107         localfile = {1999 - Schroer - New Concepts in Particle Physics from Solution of an Old Problem.pdf},
5108         title = {{Particle Physics and QFT at the Turn of the Century Old principles with new concepts (an essay on local quantum physics) }},
5109         year = {1999}
5110 }
5111 
5112 @article{Varadarajan:2000,
5113         abstract = {We revisit the quantization of U(1) holonomy algebras using the abelian C* algebra based techniques which form the mathematical underpinnings of current efforts to construct loop quantum gravity. In particular, we clarify the role of ``smeared loops'' and of Poincare invariance in the construction of Fock representations of these algebras. This enables us to critically re-examine early pioneering efforts to construct Fock space representations of linearised gravity and free Maxwell theory from holonomy algebras through an application of the (then current) techniques of loop quantum gravity.},
5114         author = {M. Varadarajan},
5115         journal = {Phys.Rev. D},
5116         keywords = {General Relativity and Quantum Cosmology (gr-qc)},
5117         localfile = {2000 - Varadarajan - Fock representations from U(1) holonomy algebras.pdf},
5118         month = jan,
5119         pages = {104001},
5120         pdf = {http://arxiv.org/pdf/gr-qc/0001050},
5121         title = {{Fock representations from U(1) holonomy algebras}},
5122         url = {http://arxiv.org/abs/gr-qc/0001050},
5123         v1descr = {Wed, 19 Jan 2000 09:02:52 GMT (21kb)},
5124         volume = {61},
5125         year = {2000}
5126 }
5127 
5128 @article{Borchers:1998,
5129         abstract = {Let M be a von Neumann algebra acting on a Hilbert space H and x in H a cyclic and separating vector for M. If there exists a half-sided translation for M, i.e. a continuous unitary group U(t) with U(t)x =x , a nonnegative spectrum fulfilling Ad U(t)M in M for t> 0 (or t< 0), then we will show that either M is of type III1 or U(t) is trivial.},
5130         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
5131         journal = {Lett. Math. Phys.},
5132         localfile = {1998 - Borchers - Half-sided Translations and the Type of von Neumann Algebras.pdf},
5133         pages = {283--290},
5134         title = {{Half-Sided Translations and the Type of von Neumann Algebras}},
5135         volume = {44},
5136         year = {1998}
5137 }
5138 
5139 @article{Fidaleo:2001,
5140         abstract = {A characterization of the quasi--split property for an inclusion of W∗ --algebras in terms of the metrically nuclear maps is established. This result extends the known characterization relative to inclusions of W∗ --factors. An application to type I von Neumann algebras is also presented.},
5141         author = {F. Fidaleo},
5142         journal = {Proc. Am. Math. Soc.},
5143         localfile = {2001 - Fidaleo - On the split property for inclusions of W-algebras.pdf},
5144         number = {1},
5145         pages = {121--127},
5146         title = {{On the Split Property for Inclusions of W*-Algebras}},
5147         volume = {130},
5148         year = {2001}
5149 }
5150 
5151 @article{EbrahimiFard:2002,
5152         abstract = {In this paper we comment on part of a recent paper by Schroer and Wiesbrock. Therein they calculate some new modular structure for the U (1)-current algebra (Weyl algebra). We point out that their findings are true in a more general setting. The split-property allows an extension to doubly-localized algebras.},
5153         author = {K. Ebrahimi-Fard},
5154         journal = {J. Phys. A},
5155         localfile = {2002 - Ebrahimi-Fard - On the relation between modular theory and geometry.pdf},
5156         pages = {6319--6328},
5157         title = {{On the relation between modular theory and geometry }},
5158         volume = {35},
5159         year = {2002}
5160 }
5161 
5162 @article{Ojima:1981,
5163         abstract = {``Therm0 field dynamics,'' allowing the Feynman diagram method to be appliedto real-time causal Green{\rq}s functions at finite temperatures (not temperature Green{\rq}s functions with imaginary times) expressed in the form of ``vacuum'' expectation values, is reconsidered in light of its connection with the algebraic formulation of statistical mechanics based upon the KMS condition. On the basis of so-obtained generalbasic formulae, the formalism is extended to the case of gauge theories, where the subsidiary condition specifying physical states, the notion of observables, and the structure of the physical subspace at finite temperatures are clarified.},
5164         author = {I. Ojima},
5165         journal = {Ann. Phys.},
5166         localfile = {1981 - Ojima - Gauge Fields at Finite Temperature - ``Thermo Field Dynamics'' and the KMS Condition and Their Extension to Gauge Theories.pdf},
5167         pages = {1--32},
5168         title = {{Gauge Fields at Finite Temperature - ``Thermo Field Dynamics'' and the KMS Condition and Their Extension to Gauge Theories}},
5169         volume = {137},
5170         year = {1981}
5171 }
5172 
5173 @phdthesis{Zahn:2007,
5174         abstract = {We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-- Feldman formalism. In particular, we compute the two--point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well--known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the φ3 and the Wess--Zumino model and show that the dis- tortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also disuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant co- ordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so--called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach.},
5175         author = {J. Zahn},
5176         keywords = {NC Minkowski; NCQFT},
5177         localfile = {2007 - Zahn - Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space - PhD-Thesis.pdf},
5178         school = {Hamburg},
5179         title = {{Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space }},
5180         year = {2007}
5181 }
5182 
5183 @article{KopfPaschke:2007,
5184         abstract = {We generalize the previously given algebraic version of ``Feynman{\rq}s proof of Maxwell{\rq}s equations'' to noncommutative configuration spaces. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such spaces, which, in contrast to most examples discussed in the literature, does not rely on a distinguished set of coordinates. We give a detailed account of several examples, e.g., C ∞ (Q) ⊗ Mn (C) which d leads to nonabelian Yang-Mills theories, and of noncommutative tori Tθ . Moreover we, examine models over the Moyal-deformed plane R2 . Assuming the θ conservation of electrical charges, we show that in this case the canonical uncer- tainty relation [xk , xl ] = igkl with metric gkl is only consistent if gkl is constant. ˙},
5185         author = {T. Kopf and M. Paschke},
5186         journal = {Preprint},
5187         localfile = {2007 - Kopf, Paschke - Generally covariant quantum mechanics on noncommutative configuration spaces.pdf},
5188         title = {{Generally covariant quantum mechanics on noncommutative configuration spaces }},
5189         year = {2007}
5190 }
5191 
5192 @article{Dybalski:2007,
5193         abstract = {It is shown that only one vacuum state can be prepared with a finite amount of energy and it appears, in particular, as a limit of physical states under large timelike translations in any theory which satisfies a phase space condition proposed in this work. This new criterion, related to the concept of additivity of energy over isolated subsystems, is verified in massive free field theory. The analysis entails very detailed results about the momentum transfer of local operators in this model.},
5194         author = {W. Dybalski},
5195         journal = {Preprint},
5196         keywords = {Mathematical Physics (math-ph)},
5197         localfile = {2007 - Dybalski - A sharpened nuclearity condition and the uniqueness of the vacuum in QFT.pdf},
5198         title = {{A sharpened nuclearity condition and the uniqueness of the vacuum in QFT }},
5199         year = {2007}
5200 }
5201 
5202 @article{MundKuckert:2004,
5203         abstract = {Recently a sufficient and necessary condition for Pauli{\rq}s spin-statistics connection in nonrelativistic quantum mechanics has been established [1]. The two-dimensional part of this result is extended to n-particle systems and reformulated and further simplified in a more geometric language.},
5204         author = {J. Mund and B. Kuckert},
5205         journal = {Preprint},
5206         localfile = {2004 - Kuckert, Mund - Spin and Statistics in Nonrelativistic Quantum Mechanics II.pdf},
5207         title = {{Spin \& Statistics in Nonrelativistic Quantum Mechanics, II }},
5208         year = {2004}
5209 }
5210 
5211 @article{Tureanu:2007,
5212         abstract = {The concept of twisted Poincar´ symmetry, as well as some implications, are reviewed. The spin-statistics relation and the nonlocality of NC QFT are discussed in the light of this quantum symmetry. The possibility of a twisted symmetry principle for quantum field and gauge theories formulated on a noncommutative space-time is also explored.},
5213         author = {A. Tureanu},
5214         journal = {Preprint},
5215         keywords = {NCQFT},
5216         localfile = {2007 - Tureanu - Twisted Poincare Symmetry and Some Implications on Noncommutative Quantum Field Theory.pdf},
5217         title = {{Twisted Poincare Symmetry and Some Implications on Noncommutative Quantum Field Theory}},
5218         year = {2007}
5219 }
5220 
5221 @article{tHooft:2007,
5222         abstract = {Abdus Salam was known for his {\lq}grand views{\rq}, grand views of science as well as grand views of society. In this talk the grand view of theoretical physics is put in perspective.},
5223         author = {G. t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft t'Hooft},
5224         journal = {Preprint},
5225         localfile = {2007 - t'Hooft - The Grand Views of Physics.pdf},
5226         title = {{The Grand View of Physics}},
5227         year = {2007}
5228 }
5229 
5230 @article{BrunettiFredenhagenVerch:2001,
5231         abstract = {A new approach to the model-independent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity, thus giving rise to the concept of a "locally covariant quantum field theory". Such locally covariant quantum field theories will be described mathematically in terms of covariant functors between the categories, on one side, of globally hyperbolic spacetimes with isometric embeddings as morphisms and, on the other side, of *-algebras with unital injective *-endomorphisms as morphisms. Moreover, locally covariant quantum fields can be described in this framework as natural transformations between certain functors. The usual Haag-Kastler framework of nets of operator-algebras over a fixed spacetime background-manifold, together with covariant automorphic actions of the isometry-group of the background spacetime, can be re-gained from this new approach as a special case. Examples of this new approach are also outlined. In case that a locally covariant quantum field theory obeys the time-slice axiom, one can naturally associate to it certain automorphic actions, called ``relative Cauchy-evolutions'', which describe the dynamical reaction of the quantum field theory to a local change of spacetime background metrics. The functional derivative of a relative Cauchy-evolution with respect to the spacetime metric is found to be a divergence-free quantity which has, as will be demonstrated in an example, the significance of an energy-momentum tensor for the locally covariant quantum field theory. Furthermore, we discuss the functorial properties of state spaces of locally covariant quantum field theories that entail the validity of the principle of local definiteness.},
5232         author = {R. Brunetti and K. Fredenhagen and R. Verch},
5233         doi = {10.1007/s00220-003-0815-7},
5234         journal = {Commun. Math. Phys.},
5235         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
5236         localfile = {2001 - Brunetti, Fredenhagen, Verch - The generally covariant locality principle - A new paradigm for local quantum physics.pdf},
5237         pages = {31--68},
5238         pdf = {http://arxiv.org/pdf/math-ph/0112041},
5239         title = {{The generally covariant locality principle -- A new paradigm for local quantum physics}},
5240         url = {http://arxiv.org/abs/math-ph/0112041},
5241         v1descr = {Wed, 19 Dec 2001 10:35:59 GMT (63kb)},
5242         volume = {237},
5243         year = {2003}
5244 }
5245 
5246 @phdthesis{Camassa:2003,
5247         abstract = {We consider quasi-free states of an abstract CCR-algebra. The well known theorem of abstract Haag duality for Fock representations is generalized to representations arising from quasi-free states not nec- essarily pure. Separating quasi-free states are characterized and the associated modular group identified as a quasi-free evolution. On the specific model of the quantum scalar free field, in any dimension and with any mass, we consider the KMS-states which turn out to be quasi-free states. Local normality is proved for massive fields or massless in dimension d ≥ 4. Generalized Haag duality is proved for a family of quasi-free states of the free field, using the theorem of abstract Haag duality, together with a theorem of duality on the one-particle space. Finally, a possible development towards Conformal Quantum Field Theory on S 1 is sketched.},
5248         author = {P. Camassa},
5249         localfile = {2003 - Camassa - Quasi-Free States and KMS States of the Scalar Free Field.pdf},
5250         school = {Rome},
5251         title = {{Quasi-Free States and KMS States of the Free Scalar Field}},
5252         year = {2003}
5253 }
5254 
5255 @phdthesis{CastroAlvaredo:2001,
5256         abstract = {The bootstrap program for 1+1-dimensional integrable Quantum Field Theories (QFT{\rq}s) is developed to a large extent for the Homogeneous sine-Gordon (HSG) models. This program can be divided into various steps, which include the computation of the exact S-matrix, Form Factors of local operators and correlation functions, as well as the identification of the operator content of the QFT and the development of various consistency checks. Taking as an input the fairly recent S-matrix proposal for the HSG-models, we confirm its consistency by carrying out both a Thermodynamic Bethe Ansatz (TBA) and a Form Factor analysis, which allow for extracting the main characteristics of the underlying Conformal Field Theory (CFT) associated to these theories. In contrast to many other 1+1-dimensional integrable models studied in the literature, the HSG-models possess two remarkable features, namely the parity breaking, both at the level of the Lagrangian and S-matrix, as well as the presence of unstable particles in the spectrum. These features have specific consequences in our analysis which are given a physical interpretation. By exploiting the Form Factor approach, we develop further the QFT advocated to the HSG-models by evaluating correlation functions of various local operators of the model. We compute the renormalisation group (RG) flow of Zamolodchikov{\rq}s c-function and ∆-functions which carry information about the RG-flow of the operator content of the underlying CFT and provide a means for the identification of the operator content of the QFT. For these functions, as well as for the scaling function computed in the TBA-context, an {\lq}staircase{\rq} pattern which can be physically interpreted, by associating the different plateaux to energy scales for the onset of stable and/or unstable particles of the model, is found. For the SU (3)2 -HSG model we show how the form factors of different local operators are interrelated by means of the momentum space cluster property. We find closed formulae for all n-particle form factors of a large class of operators of the SU (N )2 -HSG models. These formulae are expressed in terms of universal building blocks which allow both a determinant and an integral representation.},
5257         author = {O. Castro-Alvaredo},
5258         keywords = {Form Factor Program},
5259         localfile = {2001 - Castro-Alvaredo - Bootstrap Methods in 1+1-Dimensional Quantum Field Theories - the Homogeneous Sine-Gordon Models - PhD thesis.pdf},
5260         school = {Santiago de Compostela},
5261         title = {{Bootstrap Methods in 1+1-Dimensional Quantum Field Theories: the Homogeneous Sine-Gordon Models }},
5262         url = {http://www.staff.city.ac.uk/o.castro-alvaredo/heptese.pdf},
5263         year = {2001}
5264 }
5265 
5266 @lecturenotes{Schroer:2001,
5267         abstract = {arXiv:math-ph/0102018 v4 18 Apr 2001 Abstract. In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in algebraic quantum field theory'' would be equally fitting. Besides a presentation of the framework and the main results of local quantum physics these notes may serve as a guide to frontier research problems in mathematical physics with applications in particle and condensed matter physics for whose solution operator algebraic methods seem indispensable. The ultraviolet problems of the standard approach and the recent holographic aspects belong to this kind of problems.},
5268         author = {B. Schroer},
5269         localfile = {2001 - Schroer - Lectures on Algebraic Quantum Field Theory and Operator Algebras.pdf},
5270         school = {Florianopolis, Rio de Janeiro},
5271         title = {{Lectures on Algebraic Quantum Field Theory and Operator Algebras}},
5272         year = {2001}
5273 }
5274 
5275 @mastersthesis{Kniemeyer:2002,
5276         author = {O. Kniemeyer},
5277         localfile = {2002 - Kniemeyer - Untersuchungen am erzeugenden Funktional der AdS-CFT-Korrespondenz.pdf},
5278         school = {G\"{o}ttingen},
5279         title = {{Untersuchungen am erzeugenden Funktional der AdS-CFT-Korrespondenz}},
5280         year = {2002}
5281 }
5282 
5283 @article{KawahigashiLongo:2003,
5284         abstract = {We classify two-dimensional local conformal nets with parity symmetry and central charge less than 1, up to isomorphism. The maximal ones are in a bijective correspondence with the pairs of A-D-E Dynkin diagrams with the difference of their Coxeter numbers equal to 1. In our previous classification of one-dimensional local conformal nets, Dynkin diagrams D2n+1 and E7 do not appear, but now they do appear in this classification of two-dimensional local conformal nets. Such nets are also characterized as two-dimensional local conformal nets with µ-index equal to 1 and central charge less than 1. Our main tool, in addition to our previous classification results for one-dimensional nets, is 2-cohomology vanishing for certain tensor categories related to the Virasoro tensor categories with central charge less than 1.},
5285         author = {Y. Kawahigashi and R. Longo},
5286         journal = {Preprint},
5287         localfile = {2003 - Kawahigashi, Longo - Classification of Two-dimensional Local Conformal Nets with c smaller 1 and 2-cohomology Vanishing for Tensor Categories.pdf},
5288         title = {{Classification of Two-dimensional Local Conformal Nets with c < 1 and 2-cohomology Vanishing for Tensor Categories}},
5289         year = {2003}
5290 }
5291 
5292 @article{BuchholzSummers:2004,
5293         abstract = {It is shown that two observers have mutually commuting observables if they are able to prepare in each subsector of their common state space some state exhibiting no mutual correlations. This result establishes a heretofore missing link between statistical and locality (commensurability) properties of the observables of spacelike separated observers in relativistic quantum physics, envisaged four decades ago by Haag and Kastler. It is based on a discussion of coincidence experiments and suggests a physically meaningful quantitative measure of possible violations of Einstein causality.},
5294         author = {D. Buchholz and S. J. Summers},
5295         journal = {Preprint},
5296         localfile = {2004 - Buchholz, Summers - Quantum statistics and locality.pdf},
5297         title = {{Quantum Statistics and Locality }},
5298         year = {2004}
5299 }
5300 
5301 @article{ChaichianPresnajderTureanu:2004,
5302         abstract = {We present a systematic framework for noncommutative (NC) QFT within the new concept of relativistic invariance based on the notion of twisted Poincar´ symmetry (with all 10 generators), as proposed in ref. [7]. This allows to formulate and investigate all fundamental issues of relativistic QFT and offers a firm frame for the classification of particles according to the representation theory of the twisted Poincar´ symmetry and as a result for the NC versions of CPT and spin-statistics theorem, among others, discussed earlier in the literature. As a further application of this new concept of relativism we prove the NC analog of Haag{\rq}s theorem.},
5303         author = {M. Chaichian and P. Presnajder and A. Tureanu},
5304         journal = {Preprint},
5305         keywords = {NCQFT},
5306         localfile = {© symmetry and its implications.pdf},
5307         title = {{New concept of relativistic invariance in NC space-time: twisted Poincare symmetry and its implications}},
5308         year = {2004}
5309 }
5310 
5311 @article{FewsterOjimaPorrmann:2004,
5312         abstract = {In this paper we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, point- ing out that the nuclearity index in the physicists{\rq} sense vanishes for any p > 1. Our discussion of these issues suggests a new perspective, in terms of ε -entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.},
5313         author = {C. J. Fewster and I. Ojima and M. Porrmann},
5314         journal = {Preprint},
5315         localfile = {2004 - Fewster, Ojima, Porrmann - p-Nuclearity in a New Perspective.pdf},
5316         title = {{p-Nuclearity in a New Perspective}},
5317         year = {2004}
5318 }
5319 
5320 @article{HeslopSibold:2005,
5321         abstract = {arXiv:hep-th/0411161v2 Quantum field theories based on interactions which contain the Moyal star product suffer, in the general case when time does not commute with space, from several diseases: quantum equation of motions contain unusual terms, conserved currents can not be defined and the residual spacetime symmetry is not maintained. All these problems have the same origin: time ordering does not commute with taking the star product. Here we show that these difficulties can be circumvented by a new definition of time ordering: namely with respect to a light-cone variable. In particular the original spacetime symmetries SO(1, 1) × SO(2) and translation invariance turn out to be respected. Unitarity is guaranteed as well.},
5322         author = {P. Heslop and K. Sibold},
5323         journal = {Preprint},
5324         localfile = {2004 - Heslop, Sibold - Quantized equations of motion in non-commutative theories.pdf},
5325         title = {{Quantized equations of motion in non-commutative theories}},
5326         year = {2005}
5327 }
5328 
5329 @article{MundSchroerYngvason:2004,
5330         abstract = {In contrast to the usual representations of of the Poincar\'{e} group of finite spin or helicity the Wigner representations of mass zero and infinite spin are known to be incompatible with pointlike localized quantum fields. We present here a construction of quantum fields associated with these representations that are localized in semi-infinite, space-like strings. The construction is based on concepts outside the realm of Lagrangian quantization with the potential for further applications.},
5331         author = {J. Mund and B. Schroer and J. Yngvason},
5332         journal = {Phys.Lett. B},
5333         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
5334         localfile = {2004 - Mund, Schroer, Yngvason - String-Localized quantum fields from Wigner representations.pdf},
5335         pages = {156--162},
5336         pdf = {http://arxiv.org/pdf/math-ph/0402043},
5337         title = {{String-localized quantum fields from Wigner representations}},
5338         url = {http://arxiv.org/abs/math-ph/0402043},
5339         v1descr = {Mon, 16 Feb 2004 22:56:27 GMT (10kb)},
5340         v1url = {http://www.arxiv.org/abs/math-ph/0402043v1},
5341         v2descr = {Sat, 29 May 2004 13:52:34 GMT (13kb)},
5342         volume = {596},
5343         year = {2004}
5344 }
5345 
5346 @article{Ullrich:2004-1,
5347         abstract = {Abstract. We show that every tempered distribution, which is a solution of the (ho- mogenous) Klein-Gordon equation, admits a ``tame'' restriction to the characteristic (hy- per)surface {x0 + xn = 0} in (1 + n)-dimensional Minkowski space and is uniquely deter- ′ mined by this restriction. The restriction belongs to the space S∂− (Rn ) which we have ′ introduced in [16]. Moreover, we show that every element of S∂− (Rn ) appears as the ``tame'' restriction of a solution of the (homogeneous) Klein-Gordon equation. Aug 2004},
5348         author = {P. Ullrich},
5349         journal = {Preprint},
5350         localfile = {2004 - Ullrich - Uniqueness in the Characteristic Cauchy Problem of the Klein-Gordon Equation and Tame Restrictions of Generalized Functions.pdf},
5351         title = {{Uniqueness in the Characterisitc Cauchy Problem of the Klein-Gordon Equation and Tame Restrictions of Generalized Functions}},
5352         year = {2004}
5353 }
5354 
5355 @article{Gallavotti:2005,
5356         author = {G. Gallavotti},
5357         journal = {Preprint},
5358         keywords = {Constructive Quantum Field Theory},
5359         localfile = {2005 - Gallavotii - Constructive Quantum Field Theory.pdf},
5360         title = {{Constructive Quantum Field Theory}},
5361         year = {2005}
5362 }
5363 
5364 @article{DAntoniMorsella:2006,
5365         abstract = {We analyse a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R. Verch). In particular, we show that for each pair (G, N ), with G a compact Lie group and N a closed normal subgroup, there is a net of observ- able algebras which has (a subset of) DHR sectors in 1-1 correspondence with classes of irreducible representations of G, and such that only the sectors cor- responding to representations of G/N are preserved in the scaling limit. In the way of achieving this result, we derive sufficient conditions under which the scaling limit of a tensor product theory coincides with the product of the scaling limit theories.},
5366         author = {C. D'Antoni and G. Morsella},
5367         journal = {Preprint},
5368         keywords = {Algebraic Quantum Field Theory},
5369         localfile = {2006 - D'Antoni, Morsella - Scaling algebras and superselection sectors: Study of a class of models.pdf},
5370         title = {{Scaling Algebras and Superselection Sectors: Study of a Class of Models }},
5371         year = {2006}
5372 }
5373 
5374 @article{Fleischhack:2006,
5375         abstract = {We review uniqueness results for the kinematical part of loop quantum gravity. After sketching the general loop formalism, the holonomy-flux and the Weyl algebras are introduced. In both cases, then, diffeomorphism invariant representations are described.},
5376         author = {C. Fleischhack},
5377         journal = {Preprint},
5378         keywords = {Loop Quantum Gravity},
5379         localfile = {2006 - Fleischhack - Kinematical Uniqueness of Loop Quantum Gravity.pdf},
5380         title = {{Kinematical Uniqueness of Loop Quantum Gravity }},
5381         year = {2006}
5382 }
5383 
5384 @article{GieselThiemann:2006,
5385         abstract = {We introduce a new top down approach to canonical quantum gravity, called Algebraic Quantum Gravity (AQG): The quantum kinematics of AQG is determined by an abstract ∗−algebra generated by a countable set of elementary operators labelled by an algebraic graph. The quantum dynamics of AQG is governed by a single Master Constraint operator. While AQG is inspired by Loop Quantum Gravity (LQG), it differs drastically from it because in AQG there is fundamentally no topology or differential structure. A natural Hilbert space representation acquires the structure of an infinite tensor product (ITP) whose separable strong equivalence class Hilbert subspaces (sectors) are left invariant by the quantum dynamics. The missing information about the topology and differential structure of the spacetime manifold as well as about the background metric to be approximated is supplied by coherent states. Given such data, the corresponding coherent state defines a sector in the ITP which can be identified with a usual QFT on the given manifold and background. Thus, AQG contains QFT on all curved spacetimes at once, possibly has something to say about topology change and provides the contact with the familiar low energy physics. In particular, in two companion papers we develop semiclassical perturbation theory for AQG and LQG and thereby show that the theory admits a semiclassical limit whose infinitesimal gauge symmetry agrees with that of General Relativity. In AQG everything is computable with sufficient precision and no UV divergences arise due to the background independence of the fundamental combinatorial structure. Hence, in contrast to lattice gauge theory on a background metric, no continuum limit has to be taken, there simply is no lattice regulator that must be sent to zero.},
5386         author = {K. Giesel and T. Thiemann},
5387         journal = {Preprint},
5388         keywords = {Loop Quantum Gravity},
5389         localfile = {2006 - Giesel, Thiemann - Algebraic Quantum Gravity (AQG) I. Conceptual Setup.pdf},
5390         title = {{Algebraic Quantum Gravity (AQGI I. Conceptual Setup }},
5391         year = {2006}
5392 }
5393 
5394 @article{KawahigashiLongoPennigRehren:2006,
5395         abstract = {All non-local but relatively local irreducible extensions of Virasoro chiral CFTs with c < 1 are classified. The classification, which is a prerequisite for the classification of local c < 1 boundary CFTs on a two-dimensional half-space, turns out to be 1 to 1 with certain pairs of A-D-E graphs with distinguished vertices.},
5396         author = {Y. Kawahigashi and R. Longo and U. Pennig and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
5397         journal = {Preprint},
5398         keywords = {Algebraic Quantum Field Theory; Conformal Quantum Field Theory},
5399         localfile = {2006 - Kawahigashi, Longo, Pennig, Rehren - The classification of non-local chiral CFT with c less than 1.pdf},
5400         title = {{The classification of non-local chiral CFT with c<1}},
5401         year = {2006}
5402 }
5403 
5404 @article{KaminskiLewandowskiOkolow:2006,
5405         abstract = {We are concerned with the issue of quantization of a scalar field in a diffeomor- phism invariant manner. We apply the method used in Loop Quantum Gravity. It relies on the specific choice of scalar field variables referred to as the polymer variables. The quantization, in our formulation, amounts to introducing the {\lq}quantum{\rq} polymer *-star algebra and looking for positive linear functionals, called states. Assumed in our paper homeomorphism invariance allows to derive the complete class of the states. They are determined by the homeomorphism invariant states defined on the CW-complex ∗-algebra. The corresponding GNS representations of the polymer ∗-algebra and their self-adjoint extensions are derived, the equivalence classes are found and invariant subspaces characterized. In the preceding letter (the part I) we outlined those results. Here, we present the technical details.},
5406         author = {W. Kaminski and J. Lewandowski and A. Okolow},
5407         journal = {Preprint},
5408         keywords = {Loop Quantum Gravity},
5409         localfile = {2006 - Lewandowski, Kaminski, Okolow - Background independent quantizations: the scalar field II.pdf},
5410         title = {{Background independent quantizations: the scalar field II}},
5411         year = {2006}
5412 }
5413 
5414 @article{RedeiSummers:2006,
5415         abstract = {The mathematics of classical probability theory was subsumed into classical measure theory by Kolmogorov in 1933. Quantum theory as nonclassical probability theory was incorporated into the beginnings of noncommutative measure theory by von Neumann in the early thirties, as well. To precisely this end, von Neumann initiated the study of what are now called von Neumann algebras and, with Murray, made a first classification of such algebras into three types. The nonrelativistic quantum theory of systems with finitely many degrees of freedom deals exclusively with type I algebras. However, for the description of further quantum systems, the other types of von Neumann algebras are indispensable. The paper reviews quantum probability theory in terms of general von Neumann algebras, stressing the similarity of the conceptual structure of classical and noncommutative probability theories and emphasizing the correspondence between the classical and quantum concepts, though also indicating the nonclassical nature of quantum probabilistic predictions. In addition, differences between the probability theories in the type I, II and III settings are explained. A brief description is given of quantum systems for which probability theory based on type I algebras is known to be insufficient. These illustrate the physical significance of the previously mentioned differences.},
5416         author = {M. Redei and S. J. Summers},
5417         journal = {Preprint},
5418         localfile = {2006 - Redei, Summers - Quantum Probability Theory.pdf},
5419         title = {{Quantum Probability Theory}},
5420         year = {2006}
5421 }
5422 
5423 @article{Sahlmann:2006,
5424         abstract = {As a toy model for the implementation of the diffeomorphism con- straint, the interpretation of the resulting states, and the treatment of ordering ambiguities in loop quantum gravity, we consider the Hilbert space of spatially diffeomorphism invariant states for a scalar field. We give a very explicit formula for the scalar product on this space, and discuss its structure. Then we turn to the quantization of a certain class of diffeomorphism invariant quantities on that space, and discuss in detail the ordering issues involved. On a technical level these issues bear some similarity to those encountered in full loop quantum gravity.},
5425         author = {H. Sahlmann},
5426         journal = {Preprint},
5427         keywords = {Loop Quantum Gravity},
5428         localfile = {2006 - Sahlmann - Exploring the diffeomorphism invariant Hilbert space of a scalar field.pdf},
5429         title = {{Exploring the diffeomorphism invariant Hilbert space of a scalar field }},
5430         year = {2006}
5431 }
5432 
5433 @article{Thiemann:2006,
5434         abstract = {Die Weltformel ist der Heilige Gral der Physiker. Doch auf der Suche nach dieser Theorie, die alle Kr\"{a}fte vereint, sto{\ss}en sie an die Grenzen dessen, was menschlicher Geist \"{u}berhaupt noch erfassen kann. Die Schleifen-Quantengravitation gilt heute als eine aussichtsreiche Kandidatin f\"{u}r die L\"{o}sung des Problems. THOMAS THIEMANN vom MAX-PLANCK-INSTITUT F\"{U}R GRAVITATIONSPHYSIK in Potsdam ist einer ihrer weltweit f\"{u}hrenden Vertreter. Im Folgenden berichtet er \"{u}ber seine Arbeit.},
5435         author = {T. Thiemann},
5436         journal = {Preprint},
5437         keywords = {Loop Quantum Gravity; popular science},
5438         localfile = {2006 - Thiemann - Ein Universum aus brodelnden Schleifen.pdf},
5439         title = {{Ein Universum aus brodelnden Schleifen}},
5440         year = {2006}
5441 }
5442 
5443 @article{Thiemann:2006-1,
5444         abstract = {This is a (relatively) non-technical summary of the status of the quantum dynamics in Loop Quantum Gravity (LQG). We explain in detail the historical evolution of the subject and why the results obtained so far are non-trivial. The present text can be viewed in part as a response to an article by Nicolai, Peeters and Zamaklar. We also explain why certain no go conclusions drawn from a mathematically correct calculation in a recent paper by Helling et al are physically incorrect.},
5445         author = {T. Thiemann},
5446         journal = {Preprint},
5447         keywords = {Loop Quantum Gravity},
5448         localfile = {2006 - Thiemann - Loop Quantum Gravity - An Inside View.pdf},
5449         title = {{Loop Quantum Gravity: An Inside View}},
5450         year = {2006}
5451 }
5452 
5453 @article{BalogWeisz:2007,
5454         abstract = {Multi--particle form factors of local operators in integrable models in two dimensions seem to have the property that they factorize when one subset of the particles in the external states are boosted by a large rapidity with respect to the others. This remarkable property, which goes under the name of form factor clustering, was first observed by Smirnov in the O(3) non--linear σ--model and has subsequently found useful applications in integrable models without internal symmetry structure. In this paper we conjecture the nature of form factor clustering for the general O(n) σ--model and make some tests in leading orders of the 1/n expansion and for the special cases n = 3, 4.},
5455         author = {J. Balog and P. Weisz},
5456         journal = {Preprint},
5457         keywords = {Form Factor Program; kw:sigma},
5458         localfile = {2007 - Balog, Weisz - Construction and clustering properties of the 2-d non-linear sigma model form factors - O(3), O(4), large n examples.pdf},
5459         title = {{Construction and clustering properties of the 2-d non--linear σ--model form factors: O(3), O(4), large n examples}},
5460         year = 2007
5461 }
5462 
5463 @article{Baumgrtner:2007,
5464         abstract = {Thermodynamic stable interaction pair potentials which are not of the form ``positive function + real continuous function of positive type'' are presented in dimension one. Construction of such a potential in dimension two is sketched. These constructions use only elementary calculations. The mathematical background is discussed separately.},
5465         author = {B. Baumg{\"{a}}rtner},
5466         journal = {Preprint},
5467         localfile = {2007 - Baumg\"{a}rtner - Thermodynamic Stability: A note on a footnote in Ruelle's book.pdf},
5468         title = {{Thermodynamic Stability - A note on a footnote in Ruelle{\rq}s book }},
5469         year = {2007}
5470 }
5471 
5472 @article{Dybalski:2008,
5473         abstract = {A recently proposed phase space condition which comprises information about the vacuum structure and timelike asymptotic behavior of physical states is verified in massless free field theory. There follow interesting conclusions about the momentum transfer of local operators in this model.},
5474         author = {W. Dybalski},
5475         journal = {Lett.Math.Phys.},
5476         keywords = {Algebraic Quantum Field Theory; Mathematical Physics (math-ph)},
5477         pages = {217--230},
5478         pdf = {http://arxiv.org/pdf/0803.1468},
5479         title = {{A sharpened nuclearity condition for massless fields}},
5480         url = {http://arxiv.org/abs/0803.1468},
5481         v1descr = {Mon, 10 Mar 2008 18:05:55 GMT (15kb)},
5482         v1url = {http://www.arxiv.org/abs/0803.1468v1},
5483         v2descr = {Tue, 8 Jul 2008 13:04:54 GMT (15kb)},
5484         volume = {84},
5485         year = {2008}
5486 }
5487 
5488 @article{BaumgrtelJurkeLled:1995,
5489         abstract = {Using standard results on CAR- and CCR-theory and on representation theory of the Poincar\'{e} group a direct way to construct nets of local C*-algebras satisfying Haag-Kastler's axioms is given. No explicite use of any field operator or of any concrete representation of the algebra is made. The nets are associated to models of mass m greater-or-equal, slanted 0 and arbitrary spin or helicity. Finally, Fock states satisfying the spectrality condition are specified.},
5490         author = {H. Baumg{\"{a}}rtel and M. Jurke and F. Lled{\'{o}}},
5491         doi = {10.1016/0034-4877(96)83512-9},
5492         journal = {Rept. Math. Phys.},
5493         localfile = {1995 - Baumg\"{a}rtel, Jurke, Lled\'{o} - On Free Nets Over Minkowski Space.pdf},
5494         number = {1},
5495         pages = {101--127},
5496         title = {{On Free Nets Over Minkowski Space}},
5497         url = {http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VN0-3YMWKX2-J&_user=162904&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000013078&_version=1&_urlVersion=0&_userid=162904&md5=eda241c67a6639fb4bd486d8ad51ecdc},
5498         volume = {35},
5499         year = {1995}
5500 }
5501 
5502 @article{EckmannOsterwalder:1973,
5503         abstract = {Tomita's theory of modular Hilbert algebras is applied to prove the duality theorem for local von Neumann algebras in a free field theory.},
5504         author = {{{{{{{{{{{{{{{{{{{{{{{{{{J.-P.}}}}}}}}}}}}}}}}}}}}}}}}} Eckmann and K. Osterwalder},
5505         doi = {10.1016/0022-1236(73)90062-1},
5506         journal = {J. Funct. Anal.},
5507         keywords = {Modular Theory},
5508         localfile = {1972 - Eckmann, Osterwalder - An application of Tomita's theory of modular Hilbert algebras: Duality for free Bose fields.pdf},
5509         number = {1},
5510         pages = {1--12},
5511         title = {{An application of Tomita's theory of modular Hilbert algebras: Duality for free Bose fields}},
5512         url = {http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WJJ-4CRHYBM-4Y&_user=162904&_coverDate=05%2F31%2F1973&_alid=703919693&_rdoc=2&_fmt=full&_orig=search&_cdi=6880&_sort=d&_docanchor=&view=c&_ct=2&_acct=C000013078&_version=1&_urlVersion=0&_userid=162904&md5=1f33ae207b04b63eb9040ca7df0b088e},
5513         volume = {13},
5514         year = {1973}
5515 }
5516 
5517 @misc{Kopper:2005,
5518         abstract = {I give an overview over some work on rigorous renormalization theory based on the differential flow equations of the Wilson-Wegner renormalization group. I first consider massive Euclidean $\phi_4^4$-theory. The renormalization proofs are achieved through inductive bounds on regularized Schwinger functions. I present relatively crude bounds which are easily proven, and sharpened versions (which seem to be optimal as regards large momentum behaviour). Then renormalizability statements in Minkowski space are presented together with analyticity properties of the Schwinger functions. Finally I give a short description of further results.},
5519         author = {C. Kopper},
5520         keywords = {High Energy Physics - Theory (hep-th)},
5521         localfile = {2005 - Kopper - Renormalization Theory based on Flow Equations.pdf},
5522         month = aug,
5523         pdf = {http://arxiv.org/pdf/hep-th/0508143},
5524         title = {{Renormalization Theory based on Flow Equations}},
5525         url = {http://arxiv.org/abs/hep-th/0508143},
5526         v1descr = {Fri, 19 Aug 2005 19:09:01 GMT (17kb)},
5527         year = {2005}
5528 }
5529 
5530 @article{KleinLandau:1982,
5531         abstract = {Given a continuous representation of the Euclidean group in n+1 dimensions, together with a covariant system of subspaces, which satisfies Osterwalder-Schrader positivity, we construct a continuous unitary representation of the orthochronous Poincare group in n-1 dimensions satisfying the spectral condition. A similar result holds for the covering groups of the Euclidean and Poincare group.},
5532         author = {A. Klein and L. J. Landau},
5533         journal = {Commun. Math. Phys.},
5534         keywords = {kw:NC-Wick},
5535         localfile = {1983 - Klein, Landau - From the Euclidean group to the Poincar\'{e} group via Osterwalder-Schrader positivity.pdf},
5536         pages = {469--484},
5537         title = {{From the Euclidean group to the Poincar\'{e} group via Osterwalder-Schrader positivity}},
5538         url = {http://projecteuclid.org/euclid.cmp/1103922129},
5539         volume = {87},
5540         year = {1982}
5541 }
5542 
5543 @article{LscherMack:1975,
5544         abstract = {Suppose that there is given a Wightman quantum field theory (QFT) whose Euclidean Green functions are invariant under the Euclidean conformal group (5~SO e (5, 1). We show that its Hubert space of physical states carries then a unitary representation of the universal (oo-sheeted) covering group (5* of the Minkowskian conformal group SOe(4, 2)/Z2. The Wightman functions can be analytically continued to a domain of holomorphy which has as a real boundary an oo-sheeted covering M of Minkowski-space M4. It is known that 05* can act on this space M and that M admits a globally @*-invariant causal ordering; M is thus the natural space on which a globally (5*- invariant local QFT could live. We discuss some of the properties of such a theory, in particular the spectrum of the conformal Hamiltonian H = i(P° + K°). As a tool we use a generalized Hille-Yosida theorem for Lie semigroups. Such a theorem is stated and proven in Appendix C. It enables us to analytically continue contractive representations of a certain maximal subsemigroup 6 of (5 to unitary representations of ... .},
5545         author = {M. L{\"{u}}scher and G. Mack},
5546         journal = {Commun. Math. Phys.},
5547         localfile = {1975 - L\"{u}scher, Mack - Global Conformal Invariance in Quantum Field Theory.pdf},
5548         pages = {203--234},
5549         title = {{Global conformal invariance in quantum field theory}},
5550         url = {http://projecteuclid.org/euclid.cmp/1103898909},
5551         volume = {41},
5552         year = {1975}
5553 }
5554 
5555 @phdthesis{Paschke:2001,
5556         author = {M. Paschke},
5557         localfile = {2001 - Paschke - Von Nichtkommutativen Geometrien, ihren Symmetrien und etwas Hochenergiephysik.pdf},
5558         school = {Mainz},
5559         title = {{Von nichtkommutativen Geometrien, ihren Symmetrien und etwas Hochenergiephysik}},
5560         year = {2001}
5561 }
5562 
5563 @misc{Schroer:2008-1,
5564         abstract = {We remind the reader of the meaning and achievements of infraparticles which, although themselves not necessarily of zero mass, require the presence of zero mass in order get delocalized states with a singularity at the mass shell which is amalgamated with the continuum. These objects were recently rediscovered under the name unparticles pointing to their not being usual Wigner particles. The case of infraparticles also encompasses particle-like objects in conformal QFT when all multiparticle thresholds coalesce on top of each other. The infraparticle research has led to deep results and the recently discovered string-localized vector potentials have led to new interesting aspects of the infraparticle problem which are presently being investigated.},
5565         author = {B. Schroer},
5566         journal = {Preprint},
5567         keywords = {High Energy Physics - Theory (hep-th)},
5568         localfile = {2008 - Schroer - A note on Infraparticles and Unparticles.pdf},
5569         month = apr,
5570         pdf = {http://arxiv.org/pdf/0804.3563},
5571         title = {{A note on Infraparticles and Unparticles}},
5572         url = {http://arxiv.org/abs/0804.3563},
5573         v1descr = {Tue, 22 Apr 2008 19:35:38 GMT (6kb)},
5574         year = {2008}
5575 }
5576 
5577 @article{GuidoLongo:1992,
5578         author = {D. Guido and R. Longo},
5579         doi = {10.1007/BF02096548},
5580         journal = {Commun. Math. Phys.},
5581         keywords = {Algebraic Quantum Field Theory},
5582         localfile = {1992 - Guido, Longo - Relativistic invariance and charge conjugation in quantum field theory.pdf},
5583         pages = {521--551},
5584         slaccitation = {\%\%CITATION = CMPHA,148,521\\;\%\%},
5585         title = {{Relativistic invariance and charge conjugation in quantum field theory}},
5586         volume = {148},
5587         year = {1992}
5588 }
5589 
5590 @article{GayralGraciaBondiaIochumSchuckerVarilly:2004,
5591         archiveprefix = {arXiv},
5592         author = {V. Gayral and J. M. Gracia-Bondia and B. Iochum and T. Schucker and J. C. Varilly},
5593         doi = {10.1007/s00220-004-1057-z},
5594         eprint = {hep-th/0307241},
5595         journal = {Commun. Math. Phys.},
5596         keywords = {kw:NC-Wick},
5597         localfile = {2003 - Gayral, Gracia-Bondia, Iochum, Schucker, Varilly - Moyal planes are spectral triples.pdf},
5598         pages = {569--623},
5599         slaccitation = {\%\%CITATION = HEP-TH/0307241\\;\%\%},
5600         title = {{Moyal planes are spectral triples}},
5601         url = {http://arxiv.org/abs/hep-th/0307241},
5602         volume = {246},
5603         year = {2004}
5604 }
5605 
5606 @article{SwiecaVoelkel:1973,
5607         author = {J. A. Swieca and A. H. Voelkel},
5608         doi = {10.1007/BF01646134},
5609         journal = {Commun. Math. Phys.},
5610         localfile = {1973 - Swieca, V\"{o}lkel - Remarks on Conformal Invariance.pdf},
5611         pages = {319--342},
5612         slaccitation = {\%\%CITATION = CMPHA,29,319\\;\%\%},
5613         title = {{Remarks on conformal invariance}},
5614         url = {http://projecteuclid.org/euclid.cmp/1103858590},
5615         volume = {29},
5616         year = {1973}
5617 }
5618 
5619 @misc{Schroer:2008-2,
5620         abstract = {Indecomposable positive energy quantum matter comes in three forms: one massive and two massless families of which about the so called ``infinite spin'' family was little known up to recently. Using novel methods which are particularly suited for problems of localization, it was shown that this quantum matter of the third kind cannot be generated by pointlike localized fields but rather needs semiinfinite stringlike generators. A milder form of darkness which only concerns string-localized potentials in a theory with pointlike generated observables emerges from a reformulation of nonabelian gauge theory. It is the main aim of this paper to show that the ``axial gauge'' which hitherto was considered as a special gauge for a massless vectorpotentials is not at all an object of gauge theory but rather a semiinfinite spacelike string-localized covariant quantum field in a physical Hilbert space. We suggest that this reinterpretation of gauge theory in which the pointlike unphysical BRST treatment is traded with interacting stringlike potentials could lead to a conservative (within the standard model) understanding of dark matter i.e. dark matter as the invisible energy-momentum carrying part of what used to be the gauge dependent part in the pointlike gauge dependent description. The clearest indication that the axial gauge interpretation was incorrect is that the vectorpotentials fluctuates in the string direction as well as in its endpoint. PACS: 95.35+d, 11.10-z, 11.30 Cp},
5621         author = {B. Schroer},
5622         keywords = {Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
5623         localfile = {2008 - Schroer - Do confinement and darkness have the same conceptual roots - The crucial role of localization.pdf},
5624         month = apr,
5625         pdf = {http://arxiv.org/pdf/0802.3526},
5626         title = {{Do confinement and darkness have the same conceptual roots? The crucial role of localization}},
5627         url = {http://arxiv.org/abs/0802.3526},
5628         v1descr = {Mon, 25 Feb 2008 14:48:20 GMT (19kb)},
5629         v1url = {http://www.arxiv.org/abs/0802.3526v1},
5630         v2descr = {Tue, 26 Feb 2008 16:22:21 GMT (21kb)},
5631         v2url = {http://www.arxiv.org/abs/0802.3526v2},
5632         v3descr = {Thu, 24 Apr 2008 18:51:52 GMT (31kb)},
5633         year = {2008}
5634 }
5635 
5636 @article{ChaichianNishijimaSalminenTureanu:2008,
5637         abstract = {The concept of a noncommutative field is formulated based on the interplay between twisted Poincar\'{e} symmetry and residual symmetry of the Lorentz group. Various general dynamical results supporting this construction, such as the light-wedge causality condition and the integrability condition for Tomonaga-Schwinger equation, are presented. Based on this analysis, the claim of the identity between commutative QFT and noncommutative QFT with twisted Poincar\'{e} symmetry is refuted.},
5638         author = {M. Chaichian and K. Nishijima and T. Salminen and A. Tureanu},
5639         journal = {JHEP},
5640         keywords = {High Energy Physics - Theory (hep-th); NCQFT},
5641         pages = {078},
5642         pdf = {http://arxiv.org/pdf/0805.3500},
5643         title = {{Noncommutative Quantum Field Theory: A Confrontation of Symmetries}},
5644         url = {http://arxiv.org/abs/0805.3500},
5645         v1descr = {Thu, 22 May 2008 16:47:02 GMT (19kb)},
5646         volume = {0806},
5647         year = {2008}
5648 }
5649 
5650 @article{Yngvason:1986,
5651         author = {J. Yngvason},
5652         journal = {Annales Poincare Phys. Theor.},
5653         keywords = {Algebraic Quantum Field Theory},
5654         localfile = {1986 - Yngvason - Invariant states on Borchers{\rq} tensor algebra.pdf},
5655         pages = {117--145},
5656         slaccitation = {\%\%CITATION = AHPAA,45,117\\;\%\%},
5657         title = {{Invariant states on Borchers' tensor algebra}},
5658         url = {http://www.numdam.org/numdam-bin/fitem?id=AIHPA_1986__45_2_117_0},
5659         volume = {45},
5660         year = {1986}
5661 }
5662 
5663 @article{Yngvason:1981,
5664         abstract = {A class of states on Borchers' tensor algebra is constructed. These states are invariant under the translation group and fulfill the spectrum condition. This leads to a characterization of the linear span of all such states in terms of a simple continuity property.},
5665         author = {J. Yngvason},
5666         doi = {10.1007/BF01209075},
5667         journal = {Commun. Math. Phys.},
5668         keywords = {kw:NC-Wick},
5669         localfile = {1981 - Yngvason - Translationally invariant states and the spectrum ideal in the algebra of test functions for quantum fields.pdf},
5670         pages = {401},
5671         slaccitation = {\%\%CITATION = CMPHA,81,401\\;\%\%},
5672         title = {{Translationally invariant states and the spectrum ideal in the algebra of test functions for quantum fields}},
5673         url = {http://projecteuclid.org/euclid.cmp/1103920325},
5674         volume = {81},
5675         year = {1981}
5676 }
5677 
5678 @article{Yngvason:1973,
5679         abstract = {It is shown that every continuous linear functional on the field algebra can be defined by a vector in the Hubert space of some representation of the algebra. The functionals which can be written as a difference of positive ones are characterized. By an example it is shown that a positive functional on a subalgebra does not always have an extension to a positive functional on the whole algebra.},
5680         author = {J. Yngvason},
5681         doi = {10.1007/BF01646476},
5682         journal = {Commun. Math. Phys.},
5683         localfile = {1973 - Yngvason - On the Algebra of Test Functions for Field Operators - Decomposition of Linear Functionals into Positive Ones.pdf},
5684         pages = {315--333},
5685         slaccitation = {\%\%CITATION = CMPHA,34,315\\;\%\%},
5686         title = {{On the algebra of test functions for field operators. decomposition of linear functionals into positive ones}},
5687         url = {http://projecteuclid.org/euclid.cmp/1103859476},
5688         volume = {34},
5689         year = {1973}
5690 }
5691 
5692 @article{Borchers:1962,
5693         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
5694         doi = {10.1007/BF02745645},
5695         journal = {Nuovo Cimento},
5696         keywords = {kw:NC-Wick},
5697         localfile = {1962 - Borchers - On Structure of the Algebra of Field Operators.pdf},
5698         title = {{On Structure of the Algebra of Field Operators}},
5699         volume = {24},
5700         year = {1962}
5701 }
5702 
5703 @article{Franco:2005,
5704         abstract = {In this paper, we arrive at the notion of equivalence classes of a non-commutative field exploring some ideas by Soloviev to nonlocal quantum fields. Specifically, an equivalence relation between non-commutative fields is formulated by replacing the weak relative locality condition by a weak relative asymptotic commutativity property, generalizing the notion of relative locality proved by Borchers in the framework of local QFT. We restrict ourselves to the simplest case of a scalar field theory with space-space non-commutativity.},
5705         archiveprefix = {arXiv},
5706         author = {D. H. T. Franco},
5707         doi = {10.1088/0305-4470},
5708         druck = {Booklet 22.07.08},
5709         eprint = {hep-th/0404029},
5710         journal = {J. Phys.},
5711         localfile = {2005 - Franco - On the Borchers Class of a Non-Commutative Field.pdf},
5712         pages = {5799--5808},
5713         slaccitation = {\%\%CITATION = HEP-TH/0404029\\;\%\%},
5714         title = {{On the Borchers class of a non-commutative field}},
5715         volume = {A38},
5716         year = {2005}
5717 }
5718 
5719 @article{BorchersYngvason:2000,
5720         abstract = {We review the PCT-theorem and problems connected with its demonstration. We add a new proof of the PCT-theorem in the theory of local observables which is similar to that one of Jost in Wightman quantum field theory. We also look at consequences in case the PCT-symmetry is given on the algebraic level. At the end we present some examples which answer general questions and throw some light on open problems.},
5721         archiveprefix = {arXiv},
5722         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and J. Yngvason},
5723         eprint = {math-ph/0012020},
5724         localfile = {2001 - Borchers, Yngvason - On the PCT--Theorem in the Theory of Local Observables.pdf},
5725         slaccitation = {\%\%CITATION = MATH-PH/0012020\\;\%\%},
5726         title = {{On the PCT-theorem in the theory of local observables}},
5727         year = {2000}
5728 }
5729 
5730 @inproceedings{BuchholzSummers:2008,
5731         abstract = {Recently, Grosse and Lechner introduced a novel deformation procedure for non-interacting quantum field theories, giving rise to interesting examples of wedge-localized quantum fields with a non-trivial scattering matrix. In the present article we outline an extension of this procedure to the general framework of quantum field theory by introducing the concept of warped convolutions: given a theory, this construction provides wedge-localized operators which commute at spacelike distances, transform covariantly under the underlying representation of the Poincare group and admit a scattering theory. The corresponding scattering matrix is nontrivial but breaks the Lorentz symmetry, in spite of the covariance and wedge-locality properties of the deformed operators.},
5732         author = {D. Buchholz and S. J. Summers},
5733         booktitle = {{Quantum Field Theory and Beyond: Essays in Honor of Wolfhart Zimmermann}},
5734         druck = {Booklet 22.07.08},
5735         editor = {E. Seiler and K. Sibold},
5736         keywords = {Mathematical Physics (math-ph); kw:NC-Wick; kw:warping},
5737         localfile = {2008 - Buchholz, Summers - Warped Convolutions: A Novel Tool in the Construction of Quantum Field Theories.pdf},
5738         pages = {107--121},
5739         pdf = {http://arxiv.org/pdf/0806.0349},
5740         publisher = {World Scientific},
5741         title = {{Warped Convolutions: A Novel Tool in the Construction of Quantum Field Theories}},
5742         url = {http://arxiv.org/abs/0806.0349},
5743         v1descr = {Mon, 2 Jun 2008 18:28:12 GMT (17kb)},
5744         year = {2008}
5745 }
5746 
5747 @article{CareyPhillipsRennie:2007,
5748         abstract = {We review the recent construction of semifinite spectral triples for graph C^*-algebras. These examples have inspired many other developments and we review some of these such as the relation between the semifinite index and the Kasparov product, examples of noncommutative manifolds, and an index theorem in twisted cyclic theory using a KMS state.},
5749         author = {A. L. Carey and J. Phillips and A. Rennie},
5750         journal = {Preprint},
5751         keywords = {Operator Algebras (math.OA)},
5752         localfile = {2007 - Carey, Phillips, Rennie - Semifinite spectral triples associated with graph Cstar-algebras.pdf},
5753         month = jul,
5754         pdf = {http://arxiv.org/pdf/0707.3853},
5755         title = {{Semifinite Spectral Triples associated with Graph C*-Algebras}},
5756         url = {http://arxiv.org/abs/0707.3853},
5757         v1descr = {Thu, 26 Jul 2007 02:41:55 GMT (26kb)},
5758         year = {2007}
5759 }
5760 
5761 @article{GrosseVignesTourneret:2008,
5762         abstract = {We prove the perturbative renormalisability of a minimalist translation-invariant non-commutative scalar field theory. The result is based on a careful analysis of the uv/ir mixing of the non-commutative self-interacting scalar model on the four-dimensional Moyal space.},
5763         author = {H. Grosse and F. Vignes-Tourneret},
5764         journal = {Preprint},
5765         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
5766         localfile = {2008 - Grosse, Vignes-Tourneret - Minimalist translation-invariant non-commutative scalar field theory.pdf},
5767         pdf = {http://arxiv.org/pdf/0803.1035},
5768         title = {{Minimalist translation-invariant non-commutative scalar field theory}},
5769         url = {http://arxiv.org/abs/0803.1035},
5770         v1descr = {Fri, 7 Mar 2008 09:21:53 GMT (74kb,D)},
5771         volume = {arXiv:0803.1035},
5772         year = {2008}
5773 }
5774 
5775 @article{GurauMagnenRivasseauTanasa:2008,
5776         abstract = {In this paper we propose a translation-invariant scalar model on the Moyal space. We prove that this model does not suffer from the UV/IR mixing and we establish its renormalizability to all orders in perturbation theory.},
5777         author = {R. Gurau and J. Magnen and V. Rivasseau and A. Tanasa},
5778         journal = {Commun. Math. Phys.},
5779         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
5780         number = {LPT ORSAY 08-23},
5781         pages = {275--290},
5782         pdf = {http://arxiv.org/pdf/0802.0791},
5783         title = {{A translation-invariant renormalizable non-commutative scalar model}},
5784         url = {http://arxiv.org/abs/0802.0791},
5785         v1descr = {Wed, 6 Feb 2008 13:37:22 GMT (47kb)},
5786         volume = {287},
5787         year = {2009}
5788 }
5789 
5790 @article{Mund:2008-1,
5791         abstract = {Borchers has shown that in a translation covariant vacuum representation of a theory of local observables with positive energy the following holds: The (Tomita) modular objects associated with the observable algebra of a fixed wedge region give rise to a representation of the subgroup of the Poincare group generated by the boosts and the reflection associated to the wedge, and the translations. We prove here that Borchers' theorem also holds in charged sectors with (possibly non-Abelian) braid group statistics in low space-time dimensions. Our result is a crucial step towards the Bisognano-Wichmann theorem for Plektons in d=3, namely that the mentioned modular objects generate a representation of the proper Poincare group, including a CPT operator. Our main assumptions are Haag duality of the observable algebra, and translation covariance with positive energy as well as finite statistics of the sector under consideration.},
5792         author = {J. Mund},
5793         journal = {Annales Henri Poincare},
5794         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
5795         pages = {19--34},
5796         pdf = {http://arxiv.org/pdf/0806.1940},
5797         title = {{Borchers' Commutation Relations for Sectors with Braid Group Statistics in Low Dimensions}},
5798         url = {http://arxiv.org/abs/0806.1940},
5799         v1descr = {Wed, 11 Jun 2008 19:31:17 GMT (16kb)},
5800         v1url = {http://www.arxiv.org/abs/0806.1940v1},
5801         v2descr = {Thu, 12 Jun 2008 10:42:36 GMT (18kb)},
5802         v2url = {http://www.arxiv.org/abs/0806.1940v2},
5803         v3descr = {Thu, 10 Jul 2008 14:06:16 GMT (18kb)},
5804         volume = {10},
5805         year = {2009}
5806 }
5807 
5808 @article{Soloviev:2008,
5809         abstract = {We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking $O(x)=:\phi\star\phi:(x)$ as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties of the commutator [O(x),O(y)] and prove that, in the case of space-space noncommutativity, it does not vanish at spacelike separation in the noncommuting directions. However, the matrix elements of this commutator exhibit a rapid falloff along an arbitrary spacelike direction irrespective of the type of noncommutativity. We also consider the star commutator for this observable and show that it fails to vanish even at spacelike separation in the commuting directions and completely violates causality. We conclude with a brief discussion about the modified Wightman functions which are vacuum expectation values of the star products of fields at different spacetime points.},
5810         archiveprefix = {arXiv},
5811         author = {M. A. Soloviev},
5812         comments = {``wedge-locality'' in a double wedge for the deformed free field if time commutes (fixed nc parameter). nice first ideas for theta-deformations of general wightman theories.},
5813         doi = {10.1103/PhysRevD.77.125013},
5814         eprint = {0802.0997},
5815         journal = {Phys. Rev.},
5816         keywords = {kw:NC-Wick},
5817         localfile = {2008 - Soloviev - On the failure of microcausality in noncommutative field theories.pdf},
5818         pages = {125013},
5819         primaryclass = {hep-th},
5820         slaccitation = {\%\%CITATION = 0802.0997\\;\%\%},
5821         title = {{On the failure of microcausality in noncommutative field theories}},
5822         url = {http://arxiv.org/abs/0802.0997},
5823         volume = {D77},
5824         year = {2008}
5825 }
5826 
5827 @article{ChaichianMnatsakanovaTureanuVernov:2007,
5828         abstract = {It is proven that the $\star$-product of field operators implies that the space of test functions in the Wightman approach to noncommutative quantum field theory is one of the Gel'fand-Shilov spaces $S^$ with $\beta < 1/2$. This class of test functions smears the noncommutative Wightman functions, which are in this case generalized distributions, sometimes called hyperfunctions. The existence and determination of the class of the test function spaces in NC QFT is important for any rigorous treatment in the Wightman approach.},
5829         author = {M. Chaichian and M. Mnatsakanova and A. Tureanu and Yu. Vernov},
5830         journal = {JHEP},
5831         keywords = {High Energy Physics - Theory (hep-th)},
5832         number = {HIP-2007-31/TH},
5833         pages = {125},
5834         pdf = {http://arxiv.org/pdf/0706.1712},
5835         title = {{Test Functions Space in Noncommutative Quantum Field Theory}},
5836         url = {http://arxiv.org/abs/0706.1712},
5837         v1descr = {Tue, 12 Jun 2007 14:54:38 GMT (10kb)},
5838         v1url = {http://www.arxiv.org/abs/0706.1712v1},
5839         v2descr = {Wed, 16 Apr 2008 12:59:25 GMT (11kb)},
5840         v2url = {http://www.arxiv.org/abs/0706.1712v2},
5841         v3descr = {Sat, 26 Jul 2008 14:59:00 GMT (11kb)},
5842         volume = {0809},
5843         year = {2008}
5844 }
5845 
5846 @article{DoplicherFredenhagenRoberts:1994,
5847         author = {S. Doplicher and K. Fredenhagen and J. E. Roberts},
5848         doi = {10.1016/0370-2693(94)90940-7},
5849         journal = {Phys. Lett.},
5850         localfile = {1994 - Doplicher, Fredenhagen, Roberts - Space-time quantization induced by classical gravity.pdf},
5851         pages = {39--44},
5852         slaccitation = {\%\%CITATION = PHLTA,B331,39\\;\%\%},
5853         title = {{Space-time quantization induced by classical gravity}},
5854         volume = {B331},
5855         year = {1994}
5856 }
5857 
5858 @book{BogolubovLogunovTodorov:1975,
5859         author = {N. N. Bogolubov and A. A. Logunov and I. T. Todorov},
5860         localfile = {http://theory.djvu},
5861         publisher = {W. A. Benjamin, Inc.},
5862         title = {{Introduction to Axiomatic Quantum Field Theory}},
5863         year = {1975}
5864 }
5865 
5866 @article{AkoforBalachandranJoseph:2008,
5867         abstract = {We give an introductory review of quantum physics on the noncommutative spacetime called the Groenewold-Moyal plane. Basic ideas like star products, twisted statistics, second quantized fields and discrete symmetries are discussed. We also outline some of the recent developments in these fields and mention where one can search for experimental signals.},
5868         author = {E. Akofor and A. P. Balachandran and A. Joseph},
5869         journal = {Int.J.Mod.Phys. A},
5870         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA)},
5871         month = jun,
5872         pages = {1637--167},
5873         pdf = {http://arxiv.org/pdf/0803.4351},
5874         title = {{Quantum Fields on the Groenewold-Moyal Plane}},
5875         url = {http://arxiv.org/abs/0803.4351},
5876         v1descr = {Sun, 30 Mar 2008 21:52:15 GMT (131kb)},
5877         v1url = {http://www.arxiv.org/abs/0803.4351v1},
5878         v2descr = {Tue, 24 Jun 2008 18:41:23 GMT (473kb)},
5879         volume = {23},
5880         year = {2008}
5881 }
5882 
5883 @article{AkoforBalachandranJoJoseph:2007,
5884         abstract = {We show that despite the inherent non-locality of quantum field theories on the Groenewold-Moyal (GM) plane, one can find a class of ${\bf C}$, ${\bf P}$, ${\bf T}$ and ${\bf CPT}$ invariant theories. In particular, these are theories without gauge fields or with just gauge fields and no matter fields. We also show that in the presence of gauge fields, one can have a field theory where the Hamiltonian is ${\bf C}$ and ${\bf T}$ invariant while the $S$-matrix violates ${\bf P}$ and ${\bf CPT}$. In non-abelian gauge theories with matter fields such as the electro-weak and $QCD$ sectors of the standard model of particle physics, ${\bf C}$, ${\bf P}$, ${\bf T}$ and the product of any pair of them are broken while ${\bf CPT}$ remains intact for the case $\theta^{0i} =0$. (Here $x^ \star x^ - x^ \star x^ = i \theta^{\mu \nu}$, $x^$: coordinate functions, $\theta^{\mu \nu} = -\theta^{\nu \mu}=$ constant.) When $\theta^{0i} \neq 0$, it contributes to breaking also ${\bf P}$ and ${\bf CPT}$. It is known that the $S$-matrix in a non-abelian theory depends on $\theta^{\mu \nu}$ only through $\theta^{0i}$. The $S$-matrix is frame dependent. It breaks (the identity component of the) Lorentz group. All the noncommutative effects vanish if the scattering takes place in the center-of-mass frame, or any frame where $\theta^{0i}P^{\textrm{in}}_{i} = 0$, but not otherwise. ${\bf P}$ and ${\bf CPT}$ are good symmetries of the theory in this special case.},
5885         author = {E. Akofor and A. P. Balachandran and S. G. Jo and A. Joseph},
5886         journal = {JHEP},
5887         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA)},
5888         localfile = {2007 - Akofor, Balachandran, Jo, Joseph - Quantum Fields on the Groenwald-Moyal Plane: C, P, T and CPT.pdf},
5889         number = {045},
5890         pdf = {http://arxiv.org/pdf/0706.1259},
5891         title = {{Quantum Fields on the Groenewold-Moyal Plane: C, P, T and CPT}},
5892         url = {http://arxiv.org/abs/0706.1259},
5893         v1descr = {Fri, 8 Jun 2007 21:27:32 GMT (62kb)},
5894         v1url = {http://www.arxiv.org/abs/0706.1259v1},
5895         v2descr = {Tue, 19 Jun 2007 14:43:18 GMT (63kb)},
5896         v2url = {http://www.arxiv.org/abs/0706.1259v2},
5897         v3descr = {Tue, 24 Jul 2007 15:31:07 GMT (63kb)},
5898         v3url = {http://www.arxiv.org/abs/0706.1259v3},
5899         v4descr = {Thu, 26 Jul 2007 16:08:47 GMT (63kb)},
5900         v4url = {http://www.arxiv.org/abs/0706.1259v4},
5901         v5descr = {Thu, 4 Oct 2007 06:37:30 GMT (63kb)},
5902         volume = {08},
5903         year = {2007}
5904 }
5905 
5906 @article{AschieriJurcoSchuppWess:2003,
5907         archiveprefix = {arXiv},
5908         author = {P. Aschieri and B. Jurco and P. Schupp and J. Wess},
5909         doi = {10.1016/S0550-3213(02)00937-9},
5910         eprint = {hep-th/0205214},
5911         journal = {Nucl. Phys.},
5912         localfile = {2002 - Aschieri, Jurco, Schupp, Wess - Noncommutative GUTs, standard model and C,P,T..pdf},
5913         pages = {45--70},
5914         slaccitation = {\%\%CITATION = HEP-TH/0205214\\;\%\%},
5915         title = {{Non-commutative GUTs, standard model and C, P, T}},
5916         volume = {B651},
5917         year = {2003}
5918 }
5919 
5920 @article{Soloviev:2006,
5921         abstract = {We analyze functional analytic aspects of axiomatic formulations of nonlocal and noncommutative quantum field theories. In particular, we completely clarify the relation between the asymptotic commutativity condition, which ensures the CPT symmetry and the standard spin-statistics relation for nonlocal fields, and the regularity properties of the retarded Green's functions in momentum space that are required for constructing a scattering theory and deriving reduction formulas. This result is based on a relevant Paley-Wiener-Schwartz-type theorem for analytic functionals. We also discuss the possibility of using analytic test functions to extend the Wightman axioms to noncommutative field theory, where the causal structure with the light cone is replaced by that with the light wedge. We explain some essential peculiarities of deriving the CPT and spin-statistics theorems in this enlarged framework.},
5922         author = {M. A. Soloviev},
5923         druck = {Booklet 25.07.08},
5924         journal = {Theor.Math.Phys.},
5925         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
5926         localfile = {2006 - Soloviev - Axiomatic formulations of nonlocal and noncommutative field theories.pdf},
5927         month = may,
5928         number = {FIAN/TD/7-06},
5929         pages = {257--269},
5930         pdf = {http://arxiv.org/pdf/hep-th/0605249},
5931         title = {{Axiomatic formulations of nonlocal and noncommutative field theories}},
5932         url = {http://arxiv.org/abs/hep-th/0605249},
5933         v1descr = {Thu, 25 May 2006 11:48:19 GMT (14kb)},
5934         volume = {147},
5935         year = {2006}
5936 }
5937 
5938 @article{ChuFurutaInami:2006,
5939         archiveprefix = {arXiv},
5940         author = {{{{{{{{{{{{{{{{{{{{{{{{{{C.-S.}}}}}}}}}}}}}}}}}}}}}}}}} Chu and K. Furuta and T. Inami},
5941         eprint = {hep-th/0502012},
5942         journal = {Int. J. Mod. Phys.},
5943         localfile = {2006 - Chu, Furuta, Inami - Locality, Causality and Noncommutative Geometry.pdf},
5944         pages = {67--82},
5945         slaccitation = {\%\%CITATION = HEP-TH/0502012\\;\%\%},
5946         title = {{Locality, causality and noncommutative geometry}},
5947         volume = {A21},
5948         year = {2006}
5949 }
5950 
5951 @article{FrancoPolito:2005,
5952         archiveprefix = {arXiv},
5953         author = {D. H. T. Franco and C. M. M. Polito},
5954         eprint = {hep-th/0403028},
5955         journal = {J. Math. Phys.},
5956         localfile = {2004 - Franco , Polito - A New Derivation of the CPT and Spin-Statistics Theorems in Non-Commutative Field Theories.pdf},
5957         pages = {083503},
5958         slaccitation = {\%\%CITATION = HEP-TH/0403028\\;\%\%},
5959         title = {{A new derivation of the CPT and spin-statistics theorems in non-commutative field theories}},
5960         volume = {46},
5961         year = {2005}
5962 }
5963 
5964 @article{GrosseWulkenhaar:2004,
5965         archiveprefix = {arXiv},
5966         author = {H. Grosse and R. Wulkenhaar},
5967         doi = {10.1140/epjc},
5968         eprint = {hep-th/0402093},
5969         journal = {Eur. Phys. J.},
5970         keywords = {NCQFT},
5971         localfile = {2004 - Grosse, Wulkenhaar - The beta-function in duality-covariant noncommutative phi^4-theory.pdf},
5972         pages = {277--282},
5973         slaccitation = {\%\%CITATION = HEP-TH/0402093\\;\%\%},
5974         title = {{The beta-function in duality-covariant noncommutative phi**4 theory}},
5975         volume = {C35},
5976         year = {2004}
5977 }
5978 
5979 @article{DisertoriRivasseau:2007,
5980         archiveprefix = {arXiv},
5981         author = {M. Disertori and V. Rivasseau},
5982         doi = {10.1140/epjc},
5983         eprint = {hep-th/0610224},
5984         journal = {Eur. Phys. J.},
5985         localfile = {2007 - Disertori, Rivasseau - Two and Three Loops Beta Function of Non Commutative Phi^4_4 Theory.pdf},
5986         pages = {661--671},
5987         slaccitation = {\%\%CITATION = HEP-TH/0610224\\;\%\%},
5988         title = {{Two and three loops beta function of non commutative phi(4)**4 theory}},
5989         volume = {C50},
5990         year = {2007}
5991 }
5992 
5993 @article{DisertoriGurauMagnenRivasseau:2007,
5994         archiveprefix = {arXiv},
5995         author = {M. Disertori and R. Gurau and J. Magnen and V. Rivasseau},
5996         doi = {10.1016/j.physletb.2007.04.007},
5997         eprint = {hep-th/0612251},
5998         journal = {Phys. Lett.},
5999         localfile = {2007 - Disertori, Gurau, Magnen, Rivasseau - Vanishing of Beta Function of Non Commutative Phi^4_4 Theory to all orders.pdf},
6000         pages = {95--102},
6001         slaccitation = {\%\%CITATION = HEP-TH/0612251\\;\%\%},
6002         title = {{Vanishing of beta function of non commutative phi(4)**4 theory to all orders}},
6003         volume = {B649},
6004         year = {2007}
6005 }
6006 
6007 @article{Yngvason:1984,
6008         author = {J. Yngvason},
6009         doi = {10.2977/prims},
6010         journal = {Publ. RIMS, Kyoto University},
6011         keywords = {kw:NC-Wick},
6012         localfile = {1984 - Yngvason - On the Locality Ideal in the Algebra of Test Functions for Quantum Fields.pdf},
6013         number = {20},
6014         pages = {1063--1081},
6015         title = {{On the Locality Ideal in the Algebra of Test Functions for Quantum Fields}},
6016         year = {1984}
6017 }
6018 
6019 @article{LassnerUhlmann:1968,
6020         author = {G. Lassner and A. Uhlmann},
6021         journal = {Commun. Math. Phys.},
6022         localfile = {1968 - Lassner, Uhlmann - On positive functionals on algebras of test functions for quantum fields.pdf},
6023         pages = {152--159},
6024         title = {{On positive functionals on algebras of test functions for quantum fields}},
6025         volume = {7},
6026         year = {1968}
6027 }
6028 
6029 @article{HollandsWald:2008,
6030         archiveprefix = {arXiv},
6031         author = {S. Hollands and R. M. Wald},
6032         eprint = {0803.2003},
6033         journal = {Preprint},
6034         localfile = {2008 - Hollands, Wald - Axiomatic quantum field theory in curved spacetime.pdf},
6035         primaryclass = {gr-qc},
6036         slaccitation = {\%\%CITATION = 0803.2003\\;\%\%},
6037         title = {{Axiomatic quantum field theory in curved spacetime}},
6038         year = {2008}
6039 }
6040 
6041 @article{LeylandsRobertsTestard:1978,
6042         author = {P. Leylands and J. E. Roberts and D. Testard},
6043         journal = {Preprint},
6044         localfile = {1978 - Leyland, Roberts, Testard - Duality for Quantum Free Fields.pdf},
6045         title = {{Duality for Quantum Free Fields}},
6046         year = {1978}
6047 }
6048 
6049 @article{Buchholz:2008,
6050         abstract = {Buchholz' Vortrag anl\"{a}{\ss}lich der Verleihung der Max-Planck Medaille.},
6051         author = {D. Buchholz},
6052         journal = {Physik Journal},
6053         localfile = {2008 - Buchholz - Ein alternativer Zugang zur Teilchenphysik.pdf},
6054         title = {{Quantenfeldtheorie ohne Felder}},
6055         year = {2008}
6056 }
6057 
6058 @article{GrosseLechner:2008,
6059         abstract = {Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman theory, we consider special vacuum representations of its Weyl-Wigner deformed counterpart. In such representations, the effect of the noncommutativity on the basic structures of Wightman theory, in particular the covariance, locality and regularity properties of the fields, the structure of the Wightman functions, and the commutative limit, is analyzed. Despite the nonlocal structure introduced by the noncommutativity, the deformed quantum fields can still be localized in certain wedge-shaped regions, and may therefore be used to compute noncommutative corrections to two-particle S-matrix elements.},
6060         author = {H. Grosse and G. Lechner},
6061         doi = {10.1088/1126-6708},
6062         journal = {JHEP},
6063         keywords = {kw:NC-Wick; kw:warping},
6064         localfile = {2008 - Grosse, Lechner - Noncommutative Deformations of Wightman Quantum Field Theories.pdf},
6065         pages = {131},
6066         title = {{Noncommutative Deformations of Wightman Quantum Field Theories}},
6067         url = {http://arxiv.org/abs/0808.3459},
6068         volume = {09},
6069         x-color = {#199bff},
6070         year = {2008}
6071 }
6072 
6073 @techreport{GrosseVignesTourneret:2008-1,
6074         abstract = {We prove that the self-interacting scalar field on the four-dimensional degenerate Moyal plane is renormalisable to all orders when adding a suitable counterterm to the Lagrangean. Despite the apparent simplicity of the model, it raises several non trivial questions. Our result is a first step towards the definition of renormalisable quantum field theories on a non-commutative Minkowski space.},
6075         author = {H. Grosse and F. Vignes-Tourneret},
6076         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
6077         localfile = {2008 - Grosse, Vignes-Tourneret - Quantum field theory on the degenerate Moyal space.pdf},
6078         month = oct,
6079         number = {UWThPh-2008-05},
6080         pdf = {http://arxiv.org/pdf/0803.1035},
6081         title = {{Quantum field theory on the degenerate Moyal space}},
6082         url = {http://arxiv.org/abs/0803.1035},
6083         v1descr = {Fri, 7 Mar 2008 09:21:53 GMT (74kb,D)},
6084         v1url = {http://www.arxiv.org/abs/0803.1035v1},
6085         v2descr = {Tue, 7 Oct 2008 13:16:36 GMT (82kb,D)},
6086         year = {2008}
6087 }
6088 
6089 @article{FischerSzabo:2008,
6090         abstract = {We prove that a scalar quantum field theory defined on noncommutative Minkowski spacetime with noncommuting momentum coordinates is covariant with respect to the UV/IR duality which exchanges coordinates and momenta. The proof is based on suitable resonance expansions of charged noncommutative scalar fields in a background electric field, which yields an effective description of the field theory in terms of a coupled complex two-matrix model. The two independent matrix degrees of freedom ensure unitarity and manifest CT-invariance of the field theory. The formalism describes an analytic continuation of the renormalizable Grosse-Wulkenhaar models to Minkowski signature.},
6091         author = {A. Fischer and R. J. Szabo},
6092         doi = {10.1088/1126-6708},
6093         journal = {JHEP},
6094         keywords = {High Energy Physics - Theory (hep-th); kw:NC-Wick},
6095         localfile = {2008 - Fischer, Szabo - Duality covariant quantum field theory on noncommutative Minkowski space.pdf},
6096         pages = {031},
6097         pdf = {http://arxiv.org/pdf/0810.1195},
6098         title = {{Duality covariant quantum field theory on noncommutative Minkowski space}},
6099         url = {http://arxiv.org/abs/0810.1195},
6100         v1descr = {Tue, 7 Oct 2008 14:01:33 GMT (35kb)},
6101         v1url = {http://www.arxiv.org/abs/0810.1195v1},
6102         v2descr = {Mon, 3 Nov 2008 11:02:34 GMT (35kb)},
6103         v2url = {http://www.arxiv.org/abs/0810.1195v2},
6104         v3descr = {Tue, 10 Feb 2009 10:24:39 GMT (35kb)},
6105         volume = {0902},
6106         year = {2009}
6107 }
6108 
6109 @article{BuchholzHaag:1999,
6110         abstract = {We discuss the status and some perspectives of relativistic quantum physics.},
6111         author = {D. Buchholz and R. Haag},
6112         journal = {J.Math.Phys. 41 (2000) 3674-3697},
6113         keywords = {High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)},
6114         localfile = {1999 - Buchholz, Haag - The Quest for Understanding in Relativistic Quantum Physics.pdf},
6115         month = nov,
6116         pdf = {http://arxiv.org/pdf/hep-th/9910243},
6117         title = {{The Quest for Understanding in Relativistic Quantum Physics}},
6118         url = {http://arxiv.org/abs/hep-th/9910243},
6119         v1descr = {Fri, 29 Oct 1999 15:26:52 GMT (37kb)},
6120         v1url = {http://www.arxiv.org/abs/hep-th/9910243v1},
6121         v2descr = {Fri, 26 Nov 1999 14:04:49 GMT (38kb)},
6122         year = {1999}
6123 }
6124 
6125 @article{Symanzik:1966,
6126         abstract = {The analytic continuations to imaginary time of the Green's functions of local quantum field theory define Euclidean Green's functions. Use of the proper-time method allows to represent these functions as multiple Wiener integrals of functionals that obey infinite systems of coupled integral equations which are similar to, and for the particular model of a complex scalar field in quadrilinear self-interaction considered here a limiting case of, systems studied in quantum statistical mechanics by Ginibre. As a consequence, the Euclidean Green's functions can for this model be obtained by a limiting process, with temperature and density going to infinity, from the reduced density matrices of a nonrelativistic Bose gas. Reduced functionals are defined and their equations determined as a prepartory step to renormalization in the super-renormalizable cases of two and three dimensions.},
6127         author = {K. Symanzik},
6128         journal = {J. Math. Phys.},
6129         keywords = {Euclidian QFT},
6130         localfile = {1966 - Symanzik - Euclidean Quantum Field Theory. I. Equations for a Scalar Model.pdf},
6131         pages = {510--525},
6132         title = {{Euclidean Quantum Field Theory. I. Equations for a Scalar Model}},
6133         volume = {7},
6134         year = {1966}
6135 }
6136 
6137 @article{Schlingemann:1999,
6138         author = {D. Schlingemann},
6139         journal = {Preprint},
6140         localfile = {1999 - Schlingemann - Short-distance analysis for algebraic euclidean field theory.pdf},
6141         title = {{Short-distance analysis for algebraic euclidean field theory}},
6142         year = {1999}
6143 }
6144 
6145 @article{Schlingemann:1999-1,
6146         author = {D. Schlingemann},
6147         journal = {Rev. Math. Phys.},
6148         keywords = {kw:NC-Wick},
6149         localfile = {1999 - Schlingemann - From Euclidean Field Theory to Quantum Field Theory.pdf},
6150         pages = {1151--1178},
6151         title = {{From Euclidean Field Theory to Quantum Field Theory}},
6152         url = {http://arxiv.org/abs/hep-th/9802035},
6153         volume = {11},
6154         year = {1999}
6155 }
6156 
6157 @misc{RedeiSummers:2008,
6158         abstract = {We propose some formulations of the notion of ``operational independence'' of two subsystems of a larger quantum system and clarify their relation to other independence concepts in the literature. In addition, we indicate why the operational independence of quantum subsystems holds quite generally, both in nonrelativistic and relativistic quantum theory.},
6159         author = {M. Redei and S. J. Summers},
6160         journal = {Preprint},
6161         keywords = {Mathematical Physics (math-ph); Quantum Physics (quant-ph)},
6162         localfile = {2008 - Redei, Summers - When are quantum systems operationally independent.pdf},
6163         month = oct,
6164         pdf = {http://arxiv.org/pdf/0810.5294},
6165         title = {{When are quantum systems operationally independent?}},
6166         url = {http://arxiv.org/abs/0810.5294},
6167         v1descr = {Wed, 29 Oct 2008 14:49:42 GMT (13kb)},
6168         year = {2008}
6169 }
6170 
6171 @article{BorchersYngvason:1998,
6172         abstract = {For a quantum field in a thermal equilibrium state we discuss the group generated by time translations and the modular action associated with an algebra invariant under half-sided translations. The modular flows associated with the algebras of the forward light cone and a space-like wedge admit a simple geometric description in two dimensional models that factorize in light-cone coordinates. At large distances from the domain boundary compared to the inverse temperature the flow pattern is essentially the same as time translations, whereas the zero temperature results are approximately reproduced close to the edge of the wedge and the apex of the cone. Associated with each domain there is also a one parameter group with a positive generator, for which the thermal state is a ground state. Formally, this may be regarded as a certain converse of the Unruh-effect.},
6173         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and J. Yngvason},
6174         journal = {J.Math.Phys. 40 (1999) 601-624},
6175         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
6176         localfile = {1999 - Borchers, Yngvason - Modular groups of quantum fields in thermal states.pdf},
6177         month = may,
6178         number = {Erwin Schroedinger Institute preprint Nr. ESI-551},
6179         pdf = {http://arxiv.org/pdf/math-ph/9805013},
6180         title = {{Modular Groups of Quantum Fields in Thermal States}},
6181         url = {http://arxiv.org/abs/math-ph/9805013},
6182         v1descr = {Fri, 15 May 1998 10:59:22 GMT (37kb)},
6183         year = {1998}
6184 }
6185 
6186 @article{ArinshteinFateevZamolodchikov:1979,
6187         author = {A. E. Arinshtein and V. A. Fateev and A. B. Zamolodchikov},
6188         doi = {10.1016/0370-2693(79)90561-6},
6189         journal = {Phys. Lett.},
6190         pages = {389--392},
6191         slaccitation = {\%\%CITATION = PHLTA,B87,389\\;\%\%},
6192         title = {{Quantum S-Matrix of the (1+1)-Dimensional Toda Chain}},
6193         volume = {B87},
6194         year = {1979}
6195 }
6196 
6197 @techreport{FendleySaleur:1993,
6198         abstract = {These lecture notes provide an elementary introduction to the study of massless integrable quantum field theory in 1+1 dimensions using ``massless scattering''. Some previously unpublished results are also presented, including a non-perturbative study of Virasoro conserved quantities.},
6199         author = {P. Fendley and H. Saleur},
6200         keywords = {High Energy Physics - Theory (hep-th)},
6201         localfile = {1993 - Fendley, Saleur - Massless integrable quantum field theories and massless scattering in 1+1 dimensions.pdf},
6202         month = oct,
6203         number = {USC-93-022},
6204         pdf = {http://arxiv.org/pdf/hep-th/9310058},
6205         title = {{Massless integrable quantum field theories and massless scattering in 1+1 dimensions}},
6206         url = {http://arxiv.org/abs/hep-th/9310058},
6207         v1descr = {Mon, 11 Oct 1993 20:08:37 GMT (30kb)},
6208         year = {1993}
6209 }
6210 
6211 @article{FredenhagenRehrenSchroer:1992,
6212         author = {K. Fredenhagen and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren and B. Schroer},
6213         journal = {Rev. Math. Phys.},
6214         pages = {113--157},
6215         slaccitation = {\%\%CITATION = RMPHE,SI1,113\\;\%\%},
6216         title = {{Superselection sectors with braid group statistics and exchange algebras. 2. Geometric aspects and conformal covariance}},
6217         volume = {SI1},
6218         year = {1992}
6219 }
6220 
6221 @article{FredenhagenJr:1996,
6222         author = {K. Fredenhagen and M. J{\"{o}}r{\ss}},
6223         doi = {10.1007/BF02099249},
6224         journal = {Commun. Math. Phys.},
6225         localfile = {1996 - Fredenhagen, J\"{o}r{\ss} - Conformal Haag-Kastler nets, pointlike localized fields and the existence of operator product expansions.pdf},
6226         pages = {541--554},
6227         slaccitation = {\%\%CITATION = CMPHA,176,541\\;\%\%},
6228         title = {{Conformal Haag-Kastler nets, point-like localized fields and the existence of operator product expansions}},
6229         volume = {176},
6230         year = {1996}
6231 }
6232 
6233 @article{FredenhagenSchomerus:2001,
6234         archiveprefix = {arXiv},
6235         author = {S. Fredenhagen and V. Schomerus},
6236         eprint = {hep-th/0104043},
6237         slaccitation = {\%\%CITATION = HEP-TH/0104043\\;\%\%},
6238         title = {{Brane dynamics in CFT backgrounds}},
6239         year = {2001}
6240 }
6241 
6242 @article{FredenhagenSchomerus:2003,
6243         archiveprefix = {arXiv},
6244         author = {S. Fredenhagen and V. Schomerus},
6245         doi = {10.1103/PhysRevD.67.085001},
6246         eprint = {hep-th/0205011},
6247         journal = {Phys. Rev.},
6248         pages = {085001},
6249         slaccitation = {\%\%CITATION = HEP-TH/0205011\\;\%\%},
6250         title = {{On boundary RG-flows in coset conformal field theories}},
6251         volume = {D67},
6252         year = {2003}
6253 }
6254 
6255 @article{DAntoniFredenhagenKoster:2004,
6256         archiveprefix = {arXiv},
6257         author = {C. D'Antoni and K. Fredenhagen and S. Koster},
6258         doi = {10.1023/B:MATH.0000035040.57943.7e},
6259         eprint = {math-ph/0312017},
6260         journal = {Lett. Math. Phys.},
6261         pages = {239--247},
6262         slaccitation = {\%\%CITATION = MATH-PH/0312017\\;\%\%},
6263         title = {{Implementation of conformal covariance by diffeomorphism symmetry}},
6264         volume = {67},
6265         year = {2004}
6266 }
6267 
6268 @article{FredenhagenGaberdielKeller:2007,
6269         archiveprefix = {arXiv},
6270         author = {S. Fredenhagen and M. R. Gaberdiel and C. A. Keller},
6271         doi = {10.1088/1751-8113},
6272         eprint = {0707.2511},
6273         journal = {J. Phys.},
6274         pages = {13685--13710},
6275         primaryclass = {hep-th},
6276         slaccitation = {\%\%CITATION = 0707.2511\\;\%\%},
6277         title = {{Symmetries of perturbed conformal field theories}},
6278         volume = {A40},
6279         year = {2007}
6280 }
6281 
6282 @techreport{Kasprzak:2008,
6283         abstract = {We present a refinement of Rieffel Deformation of $\C^*$-algebras. We start from Rieffel data $(A,\Psi,\rho)$, where $A$ is a $\C^*$-algebra, $\rho$ is an action of abelian group $\Gamma$ on $A$ and $\Psi$ is a 2-cocycle on the dual group. Using Landstad theory of crossed product we get a deformed $\C^*$-algebra $A^\Psi$. In case of $\Gamma=\mathbb{R}^n$ we obtain a very simple proof of invariance of $\mathcal{K}$-groups under the deformation. In any case we get a simple proof that nuclearity is preserved under the deformation. We show how Rieffel deformation leads to quantum groups and investigate the duality. The general theory is illustrated by an example of deformation of $SL(2,\mathbb{C})$. The description of it, in terms of noncommutative coordinates $\hat\alpha,\hat\beta,\hat\gamma,\hat\delta$ is given.},
6284         author = {P. Kasprzak},
6285         keywords = {Operator Algebras (math.OA); Quantum Algebra (math.QA)},
6286         localfile = {2008 - Kasprzak - Rieffel Deformations via Crossed Products.pdf},
6287         month = jan,
6288         number = {KBN: 115/E-343/SPB/6.PR UE/DIE50/2005-2008},
6289         pdf = {http://arxiv.org/pdf/math/0606333},
6290         title = {{Rieffel Deformation via crossed products}},
6291         url = {http://arxiv.org/abs/math/0606333},
6292         v10descr = {Mon, 16 Jul 2007 09:57:45 GMT (34kb)},
6293         v10url = {http://www.arxiv.org/abs/math/0606333v10},
6294         v11descr = {Fri, 30 Nov 2007 09:05:28 GMT (35kb)},
6295         v11url = {http://www.arxiv.org/abs/math/0606333v11},
6296         v12descr = {Fri, 4 Jan 2008 12:51:58 GMT (33kb)},
6297         v1descr = {Wed, 14 Jun 2006 10:49:53 GMT (28kb)},
6298         v1url = {http://www.arxiv.org/abs/math/0606333v1},
6299         v2descr = {Tue, 20 Jun 2006 13:49:00 GMT (30kb)},
6300         v2url = {http://www.arxiv.org/abs/math/0606333v2},
6301         v3descr = {Wed, 21 Jun 2006 16:31:10 GMT (31kb)},
6302         v3url = {http://www.arxiv.org/abs/math/0606333v3},
6303         v4descr = {Fri, 25 Aug 2006 14:53:21 GMT (31kb)},
6304         v4url = {http://www.arxiv.org/abs/math/0606333v4},
6305         v5descr = {Wed, 30 Aug 2006 16:29:47 GMT (31kb)},
6306         v5url = {http://www.arxiv.org/abs/math/0606333v5},
6307         v6descr = {Tue, 7 Nov 2006 13:00:38 GMT (31kb)},
6308         v6url = {http://www.arxiv.org/abs/math/0606333v6},
6309         v7descr = {Fri, 24 Nov 2006 18:01:18 GMT (33kb)},
6310         v7url = {http://www.arxiv.org/abs/math/0606333v7},
6311         v8descr = {Mon, 27 Nov 2006 12:28:12 GMT (33kb)},
6312         v8url = {http://www.arxiv.org/abs/math/0606333v8},
6313         v9descr = {Tue, 28 Nov 2006 00:08:07 GMT (33kb)},
6314         v9url = {http://www.arxiv.org/abs/math/0606333v9},
6315         year = {2008}
6316 }
6317 
6318 @article{Rieffel:1990,
6319         author = {M. A. Rieffel},
6320         journal = {Proc. Symp. Pure Math.},
6321         localfile = {1990 - Rieffel - Deformation Quantization and Operator Algebras.pdf},
6322         number = {51},
6323         pages = {411--423},
6324         title = {{Deformation Quantization and Operator Algebras}},
6325         year = {1990}
6326 }
6327 
6328 @techreport{Waldmann:2004,
6329         abstract = {In this review we discuss various aspects of representation theory in deformation quantization starting with a detailed introduction to the concepts of states as positive functionals and the GNS construction. But also Rieffel induction of representations as well as strong Morita equivalence, the Dirac monopole and the strong Picard groupoid are discussed.},
6330         author = {S. Waldmann},
6331         keywords = {Mathematical Physics (math-ph); Quantum Algebra (math.QA)},
6332         localfile = {2004 - Waldmann - States and representations in deformation quantization.pdf},
6333         month = aug,
6334         number = {FR-THEP 2004/15},
6335         pdf = {http://arxiv.org/pdf/math/0408217},
6336         title = {{States and representations in deformation quantization}},
6337         url = {http://arxiv.org/abs/math/0408217},
6338         v1descr = {Tue, 17 Aug 2004 08:30:03 GMT (70kb)},
6339         year = {2004}
6340 }
6341 
6342 @article{HellerNeumaierWaldmann:2006,
6343         abstract = {Locally noncommutative spacetimes provide a refined notion of noncommutative spacetimes where the noncommutativity is present only for small distances. Here we discuss a non-perturbative approach based on Rieffel's strict deformation quantization. To this end, we extend the usual C*-algebraic results to a pro-C*-algebraic framework.},
6344         author = {J. G. Heller and N. Neumaier and S. Waldmann},
6345         journal = {Lett. Math. Phys.},
6346         keywords = {Mathematical Physics (math-ph); Quantum Algebra (math.QA); kw:local-ncqft},
6347         localfile = {2006 - Heller, Neumaier, Waldmann - A C-Algebraic Model for Locally Noncommutative Spacetimes.pdf},
6348         pages = {257--272},
6349         pdf = {http://arxiv.org/pdf/math/0609850},
6350         title = {{A C*-Algebraic Model for Locally Noncommutative Spacetimes}},
6351         url = {http://arxiv.org/abs/math/0609850},
6352         v1descr = {Fri, 29 Sep 2006 18:56:33 GMT (17kb)},
6353         volume = {80},
6354         year = {2007}
6355 }
6356 
6357 @techreport{Waldmann:1999,
6358         abstract = {In the framework of deformation quantization we apply the formal GNS construction to find representations of the deformed algebras in pre-Hilbert spaces over $\mathbb C[[\lambda]]$ and establish the notion of local operators in these pre-Hilbert spaces. The commutant within the local operators is used to distinguish `thermal' from `pure' representations. The computation of the local commutant is exemplified in various situations leading to the physically reasonable distinction between thermal representations and pure ones. Moreover, an analogue of von Neumann's double commutant theorem is proved in the particular situation of a GNS representation with respect to a KMS functional and for the Schr\"{o}dinger representation on cotangent bundles. Finally we prove a formal version of the Tomita-Takesaki theorem.},
6359         author = {S. Waldmann},
6360         keywords = {Mathematical Physics (math-ph); Quantum Algebra (math.QA); Symplectic Geometry (math.SG)},
6361         localfile = {1999 - Waldmann - Locality in GNS Representations of Deformation Quantization.pdf},
6362         month = mar,
6363         number = {FR-THEP-99/2},
6364         pdf = {http://arxiv.org/pdf/math/9903053},
6365         title = {{Locality in GNS Representations of Deformation Quantization}},
6366         url = {http://arxiv.org/abs/math/9903053},
6367         v1descr = {Tue, 9 Mar 1999 21:46:42 GMT (35kb)},
6368         year = {1999}
6369 }
6370 
6371 @misc{Lled:2009,
6372         abstract = {The present article contains a short introduction to Modular Theory for von Neumann algebras with a cyclic and separating vector. It includes the formulation of the central result in this area, the Tomita-Takesaki theorem, and several of its consequences. We illustrate this theory through several elementary examples. We also present more elaborate examples and compute modular objects for a discrete crossed product and for the algebra of canonical anticommutation relations (CAR-algebra) in a Fock representation.},
6373         author = {F. Lled{\'{o}}},
6374         keywords = {Mathematical Physics (math-ph); Operator Algebras (math.OA)},
6375         localfile = {2009 - Lledo - Modular Theory by Example.pdf},
6376         month = jan,
6377         pdf = {http://arxiv.org/pdf/0901.1004},
6378         title = {{Modular Theory by example}},
6379         url = {http://arxiv.org/abs/0901.1004},
6380         v1descr = {Thu, 8 Jan 2009 10:10:53 GMT (27kb)},
6381         year = {2009}
6382 }
6383 
6384 @misc{BostelmannDAntoniMorsella:2008,
6385         abstract = {Quantum field theories, at short scales, can be approximated by a scaling limit theory. In this approximation, an additional symmetry is gained, namely dilation covariance. To understand the structure of this dilation symmetry, we investigate it in a nonperturbative, model independent context. To that end, it turns out to be necessary to consider non-pure vacuum states in the limit. These can be decomposed into an integral of pure states; we investigate how the symmetries and observables of the theory behave under this decomposition. In particular, we consider several natural conditions of increasing strength that yield restrictions on the decomposed dilation symmetry.},
6386         author = {H. Bostelmann and C. D'Antoni and G. Morsella},
6387         keywords = {Mathematical Physics (math-ph); Algebraic Quantum Field Theory},
6388         localfile = {2008 - Bostelmann, D'Antoni, Morsella - On dilation symmetries arising from scaling limits.pdf},
6389         month = dec,
6390         pdf = {http://arxiv.org/pdf/0812.4762},
6391         title = {{On dilation symmetries arising from scaling limits}},
6392         url = {http://arxiv.org/abs/0812.4762},
6393         v1descr = {Sat, 27 Dec 2008 18:52:22 GMT (47kb)},
6394         year = {2008}
6395 }
6396 
6397 @misc{BostelmannFewster:2008,
6398         abstract = {Quantum inequalities are lower bounds for local averages of quantum observables that have positive classical counterparts, such as the energy density or the Wick square. We establish such inequalities in general (possibly interacting) quantum field theories on Minkowski space, using nonperturbative techniques. Our main tool is a rigorous version of the operator product expansion.},
6399         author = {H. Bostelmann and C. J. Fewster},
6400         keywords = {Mathematical Physics (math-ph)},
6401         localfile = {2008 - Bostelmann, Fewster - Quantum Inequalities from Operator Product Expansions.pdf},
6402         month = dec,
6403         pdf = {http://arxiv.org/pdf/0812.4760},
6404         title = {{Quantum Inequalities from Operator Product Expansions}},
6405         url = {http://arxiv.org/abs/0812.4760},
6406         v1descr = {Sat, 27 Dec 2008 19:15:02 GMT (43kb)},
6407         year = {2008}
6408 }
6409 
6410 @article{KaschekNeumaierWaldmann:2009,
6411         abstract = {In this paper we consider C*-algebraic deformations a la Rieffel and show that every state of the undeformed algebra can be deformed into a state of the deformed algebra in the sense of a continuous field of states. The construction is explicit and involves a convolution operator with a particular Gauss function.},
6412         author = {D. Kaschek and N. Neumaier and S. Waldmann},
6413         doi = {10.4171/JNCG},
6414         journal = {J. Noncommutative Geometry},
6415         keywords = {Astrophysics (astro-ph); kw:local-ncqft; Mathematical Physics (math-ph); Operator Algebras (math.OA)},
6416         localfile = {2008 - Kaschek, Neumaier, Waldmann - Complete Positivity of Rieffel's Deformation Quantization by Actions of Rd.pdf},
6417         month = nov,
6418         pages = {361--375},
6419         pdf = {http://arxiv.org/pdf/0809.2206},
6420         title = {{Complete Positivity of Rieffel's Deformation Quantization by Actions of $R^d$}},
6421         url = {http://arxiv.org/abs/0809.2206},
6422         v1descr = {Fri, 12 Sep 2008 12:57:53 GMT (15kb)},
6423         v1url = {http://www.arxiv.org/abs/0809.2206v1},
6424         v2descr = {Thu, 25 Sep 2008 08:52:24 GMT (15kb)},
6425         v2url = {http://www.arxiv.org/abs/0809.2206v2},
6426         v3descr = {Mon, 17 Nov 2008 08:49:27 GMT (16kb)},
6427         volume = {3},
6428         year = {2009}
6429 }
6430 
6431 @article{Wyss:1972,
6432         author = {W. Wyss},
6433         doi = {10.1007/BF01645693},
6434         journal = {Commun. Math. Phys.},
6435         localfile = {1972 - Wyss - The Field algebra and its positive linear functionals.pdf},
6436         pages = {223--234},
6437         slaccitation = {\%\%CITATION = CMPHA,27,223\\;\%\%},
6438         title = {{The field algebra and its positive linear functionals}},
6439         volume = {27},
6440         year = {1972}
6441 }
6442 
6443 @article{Florig:1998,
6444         abstract = {We give a simplified proof of the following important theorem,which is due to Borchers. Let M be a von Neumann algebra with cyclic and separating vector and let U(t), t ∈ R, be a group with positive generator, which leaves fixed and induces for positive arguments endomorphisms of M. The modular group of (M, ) acts then as dilatations on this group. Our proof can also be applied to half-sided modular inclusions.},
6445         author = {M. Florig},
6446         doi = {10.1023/A:1007546507392},
6447         journal = {Lett. Math. Phys.},
6448         localfile = {1998 - Florig - On Borchers' theorem.pdf},
6449         pages = {289--293},
6450         slaccitation = {\%\%CITATION = LMPHD,46,289\\;\%\%},
6451         title = {{On Borchers' theorem}},
6452         volume = {46},
6453         year = {1998}
6454 }
6455 
6456 @article{Piacitelli:2009,
6457         abstract = {In this letter we wish to clarify in which sense the tensor nature of the commutation relations [x^mu,x^nu]=i theta ^{mu nu} underlying Minkowski spacetime quantisation cannot be suppressed even in the twisted approach to Lorentz covariance. We then address the vexata quaestio ``why theta''?},
6458         author = {G. Piacitelli},
6459         journal = {Preprint},
6460         localfile = {2009 - Piacitelli - Twisted Covariance vs Weyl Quantisation.pdf},
6461         title = {{Twisted Covariance vs Weyl Quantisation}},
6462         year = {2009}
6463 }
6464 
6465 @article{BievreMerkli:2006,
6466         abstract = {We give a complete and rigorous proof of the Unruh effect, in the following form. We show that the state of a two-level system, uniformly accelerated with proper acceleration $a$, and coupled to a scalar bose field initially in the Minkowski vacuum state will converge, asymptotically in the detector's proper time, to the Gibbs state at inverse temperature $\beta=\frac{2\pi}{a}$. The result also holds if the field and detector are initially in an excited state. We treat the problem as one of return to equilibrium, exploiting in particular that the Minkowski vacuum is a KMS state with respect to Lorentz boosts. We then use the recently developed spectral techniques to prove the stated result.},
6467         author = {S. De Bievre and M. Merkli},
6468         journal = {Class.Quant.Grav.23:6525-6542,2006},
6469         keywords = {Mathematical Physics (math-ph)},
6470         localfile = {2006 - De Bievre, Merkli - The Unruh effect revisited.pdf},
6471         month = apr,
6472         pdf = {http://arxiv.org/pdf/math-ph/0604023},
6473         title = {{The Unruh effect revisited}},
6474         url = {http://arxiv.org/abs/math-ph/0604023},
6475         v1descr = {Tue, 11 Apr 2006 12:50:05 GMT (22kb)},
6476         year = {2006}
6477 }
6478 
6479 @misc{Summers:2008-2,
6480         abstract = {The analyzability of the universe into subsystems requires a concept of the ``independence'' of the subsystems, of which the relativistic quantum world supports many distinct notions which either coincide or are trivial in the classical setting. The multitude of such notions and the complex relations between them will only be adumbrated here. The emphasis of the discussion is placed upon the warrant for and the consequences of a particular notion of subsystem independence, which, it is proposed, should be viewed as primary and, it is argued, provides a reasonable framework within which to sensibly speak of relativistic quantum subsystems.},
6481         author = {S. J. Summers},
6482         keywords = {Algebraic Quantum Field Theory; Mathematical Physics (math-ph); Operator Algebras (math.OA); Quantum Physics (quant-ph)},
6483         localfile = {2008 - Summers - Subsystems and Independence in Relativistic Microscopic Physics.pdf},
6484         month = dec,
6485         pdf = {http://arxiv.org/pdf/0812.1517},
6486         title = {{Subsystems and Independence in Relativistic Microscopic Physics}},
6487         url = {http://arxiv.org/abs/0812.1517},
6488         v1descr = {Mon, 8 Dec 2008 16:32:42 GMT (22kb)},
6489         year = {2008}
6490 }
6491 
6492 @phdthesis{Dybalski:2009,
6493         abstract = {This Thesis presents some physically motivated criteria for the existence of particles and infra-particles in a given quantum field theory. It is based on a refined spectral theory of automorphism groups describing the energy-momentum transfer of local observables. In particular, a novel decomposition of the algebra of local observables into spectral subspaces is constructed. Apart from the counterparts of the pure-point and absolutely continuous subspaces, familiar from the spectral theory of operators, there appears a new 'point-continuous' subspace. It belongs to the singular-continuous part of the decomposition, but is finite-dimensional in a large class of models; its dimension carries information about the infrared structure of a theory. It is shown that this point-continuous subspace is trivial in all theories complying with a regularity condition proposed in this work. Moreover, this condition entails the existence of particles if the theory admits a stress-energy tensor. The uniqueness of the decomposition of the algebra of observables into the pure-point and continuous subspace is established by proving an ergodic theorem for automorphism groups. The proof is based on physically motivated phase space conditions which have a number of interesting consequences pertaining to the vacuum structure such as the convergence of physical states to a unique vacuum under large timelike translations.},
6494         author = {W. Dybalski},
6495         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
6496         localfile = {2008 - Dybalski - Spectral Theory of Automorphism Groups and Particle Structures in Quantum Field Theory.pdf},
6497         month = jan,
6498         pdf = {http://arxiv.org/pdf/0901.3127},
6499         school = {G\"{o}ttingen},
6500         title = {{Spectral Theory of Automorphism Groups and Particle Structures in Quantum Field Theory}},
6501         url = {http://arxiv.org/abs/0901.3127},
6502         v1descr = {Tue, 20 Jan 2009 19:46:48 GMT (135kb)},
6503         year = {2009}
6504 }
6505 
6506 @book{Rudin:1970,
6507         author = {W. Rudin},
6508         keywords = {Analysis; Funktionentheorie},
6509         localfile = {http://analysis.djvu},
6510         title = {{Real and complex analysis}},
6511         year = {1970}
6512 }
6513 
6514 @book{KadisonRingrose:1983,
6515         author = {R. V. Kadison and J. R. Ringrose},
6516         keywords = {Operatoralgebren; Book},
6517         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Kadison, Ringrose - Fundamentals of the Theory of Operator Algebras I - Elementary Theory.pdf},
6518         title = {{Fundamentals of the Theory of Operator Algebras I - Elementary Theory}},
6519         year = {1983}
6520 }
6521 
6522 @book{KadisonRingrose:1986,
6523         author = {R. V. Kadison and J. R. Ringrose},
6524         keywords = {Operatoralgebren; Book},
6525         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Kadison, Ringrose - Fundamentals of the Theory of Operator Algebras II - Advanced Theory.pdf},
6526         title = {{Fundamentals of the Theory of Operator Algebras II - Advanced Theory}},
6527         year = {1986}
6528 }
6529 
6530 @book{Landi:2002,
6531         author = {G. Landi},
6532         keywords = {Nichtkommutative Geometrie; Book},
6533         localfile = {/home/gandalf/Physik/Lecture Notes/1997 - Landi - An Introduction to Noncommutative Spaces and their Geometry.pdf},
6534         title = {{An Introduction to Noncommutative Spaces and their Geometries}},
6535         year = {2002}
6536 }
6537 
6538 @book{BaezSegalZhou:1992,
6539         author = {J. Baez and I. E. Segal and Z. Zhou},
6540         keywords = {Algebraische QFT; Book; Konstruktive QFT},
6541         localfile = {http://theory.djvu},
6542         title = {{Introduction to Algebraic and Constructive Quantum Field Theory}},
6543         year = {1992}
6544 }
6545 
6546 @book{BratteliRobinson:1987,
6547         author = {O. Bratteli and D. W. Robinson},
6548         keywords = {Book; Operatoralgebren; Quantenstatistik},
6549         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Bratteli, Robinson - Operator Algebras and Quantum Statistical Mechanics. Vol. 1.djvu},
6550         title = {{Operator Algebras and Quantum Statistical Mechanics I}},
6551         year = {1987}
6552 }
6553 
6554 @book{BratteliRobinson:1997,
6555         author = {O. Bratteli and D. W. Robinson},
6556         keywords = {Book; Operatoralgebren; Quantenstatistik},
6557         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Bratteli, Robinson - Operator Algebras and Quantum Statistical Mechanics. Vol. 2.djvu},
6558         publisher = {Springer},
6559         title = {{Operator Algebras and Quantum Statistical Mechanics II}},
6560         year = {1997}
6561 }
6562 
6563 @book{Haag:1996A,
6564         author = {R. Haag},
6565         edition = {2},
6566         keywords = {Algebraische QFT; Book; kw:NC-Wick; QFT},
6567         localfile = {http://algebras.djvu},
6568         publisher = {Springer},
6569         title = {{Local Quantum Physics - Fields, Particles, Algebras}},
6570         year = {1996}
6571 }
6572 
6573 @book{Jost:1965,
6574         author = {R. Jost},
6575         keywords = {Book; QFT; Wightman-QFT},
6576         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Jost - General theory of quantized fields (AMS, 1964)(L)(T)(86s).djvu},
6577         title = {{The General Theory of Quantized Fields}},
6578         year = {1965}
6579 }
6580 
6581 @phdthesis{Boller:2002,
6582         author = {S. Boller},
6583         keywords = {Modular Theory; Operatoralgebren},
6584         localfile = {2002 - Boller - Spectral Theory of Modular Operators for von Neumann Algebras and Related Inverse Problems.pdf},
6585         school = {Leipzig},
6586         title = {{Spectral Theory of Modular Operators for von Neumann Algebras and Related Inverse Problems}},
6587         year = {2002}
6588 }
6589 
6590 @article{LeitzMartiniWollenberg:2000,
6591         author = {M. Leitz-Martini and M. Wollenberg},
6592         journal = {Z. Anal. Anw.},
6593         keywords = {Algebraische QFT; Operatoralgebren},
6594         localfile = {2000 - Leitz-Martini, Wollenberg - Notes on Modular Conjugations of von Neumann Factors.pdf},
6595         number = {19},
6596         pages = {13--22},
6597         title = {{Notes on Modular Conjugations of von Neumann Factors}},
6598         url = {http://www.emis.de/journals/ZAA/1901/2.html},
6599         year = {2000}
6600 }
6601 
6602 @misc{Piacitelli:2009-1,
6603         abstract = {We discuss twisted covariance over the noncommutative spacetime algebra generated by the relations [q\_theta^mu,\q\_theta^nu]=i theta^{mu nu}, where the matrix theta is treated as fixed (not a tensor), and we refrain from using the asymptotic Moyal expansion of the twists. We show that the tensor nature of theta is only hidden in the formalism: in particular if theta fulfils the DFR conditions, the twisted Lorentz covariant model of the flat quantum spacetime may be equivalently described in terms of the DFR model, if we agree to discard a huge non invariant set of localisation states; it is only this last step which, if taken as a basic assumption, severely breaks the relativity principle. We also will show that the above mentioned, relativity breaking, ad hoc rejection of localisation states is an independent, unnecessary assumption, as far as some popular approaches to quantum field theory on the quantum Minkowski spacetime are concerned. The above should raise some concerns about speculations on possible observable consequences of arbitrary choices of theta in arbitrarily selected privileged frames.},
6604         author = {G. Piacitelli},
6605         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
6606         localfile = {2009 - Piacitelli - Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model.pdf},
6607         month = feb,
6608         pdf = {http://arxiv.org/pdf/0902.0575},
6609         title = {{Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model}},
6610         url = {http://arxiv.org/abs/0902.0575},
6611         v1descr = {Tue, 3 Feb 2009 18:22:47 GMT (27kb)},
6612         year = {2009}
6613 }
6614 
6615 @book{Takesaki:2001,
6616         author = {M. Takesaki},
6617         keywords = {Operatoralgebren},
6618         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Takesaki M. Theory of operator algebras 1 (Enc.Math.Sci.124, Springer, 2001)(ISBN 354042248X)(600dpi)(T)(435s)_MCf_.djvu},
6619         publisher = {Springer},
6620         title = {{Theory of Operator Algebras I}},
6621         year = {2001}
6622 }
6623 
6624 @book{Takesaki:2003,
6625         author = {M. Takesaki},
6626         keywords = {Operatoralgebren},
6627         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Takesaki M. Theory of operator algebras 2 (Enc.Math.Sci.125, Springer, 2003)(ISBN 354042914X)(600dpi)(T)(540s)_MCf_.djvu},
6628         publisher = {Springer},
6629         title = {{Theory of Operator Algebras II}},
6630         year = {2003}
6631 }
6632 
6633 @book{Takesaki:2003-1,
6634         author = {M. Takesaki},
6635         keywords = {Operatoralgebren},
6636         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Takesaki M. Theory of operator algebras 3 (Enc.Math.Sci.127, Springer, 2003)(ISBN 3540429131)(600dpi)(T)(570s)_MCf_.djvu},
6637         publisher = {Springer},
6638         title = {{Theory of Operator Algebras III}},
6639         year = {2003}
6640 }
6641 
6642 @book{Connes:1990,
6643         author = {A. Connes},
6644         keywords = {Nichtkommutative Geometrie},
6645         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Connes - Noncommutative Geometry.pdf},
6646         publisher = {InterEditions Paris},
6647         title = {{Noncommutative Geometry}},
6648         year = {1990}
6649 }
6650 
6651 @book{ReedSimon:1972,
6652         author = {M. Reed and B. Simon},
6653         keywords = {Functional Analysis},
6654         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Reed, Simon - Methods of Modern Mathematical Physics I - Functional Analysis.pdf},
6655         publisher = {Academic Press},
6656         title = {{Methods of Modern Mathematical Physics I - Functional Analysis}},
6657         year = {1972}
6658 }
6659 
6660 @book{ReedSimon:1975,
6661         author = {M. Reed and B. Simon},
6662         keywords = {Analysis; Functional Analysis; kw:NC-Wick},
6663         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Reed, Simon - Methods of Modern Mathematical Physics II - Fourier Analysis, Self-Adjointness.pdf},
6664         publisher = {Academic Press},
6665         title = {{Methods of Modern Mathematical Physics II - Fourier Analysis}},
6666         year = {1975}
6667 }
6668 
6669 @book{ReedSimon:1979,
6670         author = {M. Reed and B. Simon},
6671         keywords = {Analysis; Functional Analysis},
6672         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Reed, Simon - Methods of Modern Mathematical Physics III - Scattering Theory.pdf},
6673         publisher = {Academic Press},
6674         title = {{Methods of Modern Mathematical Physics III - Scattering Theory}},
6675         year = {1979}
6676 }
6677 
6678 @book{ReedSimon:1978,
6679         author = {M. Reed and B. Simon},
6680         keywords = {Analysis; Functional Analysis},
6681         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Reed, Simon - Methods of Modern Mathematical Physics IV - Analysis of Operators.pdf},
6682         publisher = {Academic Press},
6683         title = {{Methods of Modern Mathematical Physics IV - Analysis of Operators}},
6684         year = {1978}
6685 }
6686 
6687 @book{Conway:1978,
6688         address = {New York, Heidelberg, Berlin},
6689         author = {J.B. Conway},
6690         edition = {2},
6691         keywords = {Analysis; komplexe Analysis},
6692         localfile = {http://i.djvu},
6693         publisher = {Springer},
6694         title = {{Functions of One Complex Variable}},
6695         year = {1978}
6696 }
6697 
6698 @book{vonNeumann:1968,
6699         author = {J. {von Neumann}},
6700         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Neumann - Mathematische Grundlagen der Quantenmechanik.pdf},
6701         publisher = {Springer},
6702         title = {{Mathematische Grundlagen der Quantenmechanik}},
6703         year = {1968}
6704 }
6705 
6706 @book{Landsman:1998,
6707         address = {New York, Heidelberg, Berlin},
6708         author = {N. P. Landsman},
6709         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Landsman - Mathematical topics between classical and quantum mechanics.djvu},
6710         publisher = {Springer},
6711         title = {{Mathematical Topics Between Classical and Quantum Mechanics}},
6712         year = {1998}
6713 }
6714 
6715 @article{Uhlmann:1962,
6716         author = {A. Uhlmann},
6717         journal = {Wissenschaftliche Zeitschrift der Karl-Marx-Universit\"{a}t Leipzig},
6718         keywords = {kw:NC-Wick},
6719         localfile = {1962 - Uhlmann - \"{U}ber die Definition der Quantenfelder nach Wightman und Haag.pdf},
6720         pages = {213--217},
6721         title = {{\"{U}ber die Definition der Quantenfelder nach Wightman und Haag}},
6722         volume = {2},
6723         year = {1962}
6724 }
6725 
6726 @inproceedings{Borchers:1972,
6727         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
6728         booktitle = {{Statistical mechanics and field theory}},
6729         editor = {R. N. Sen and C. Weil},
6730         localfile = {1972 - Borchers - Algebraic Aspects of Wightman Field Theory.pdf},
6731         publisher = {Halsted Press},
6732         series = {{Lectures given at the 1971 Haifa Summer School}},
6733         title = {{Algebraic Aspects of Wightman Quantum Field Theory}},
6734         year = {1972}
6735 }
6736 
6737 @article{BorrisVerch:2008,
6738         abstract = {The quantized free Dirac field is considered on Minkowski spacetime (of general dimension). The Dirac field is coupled to an external scalar potential whose support is finite in time and which acts by a Moyal-deformed multiplication with respect to the spatial variables. The Moyal-deformed multiplication corresponds to the product of the algebra of a Moyal plane described in the setting of spectral geometry. It will be explained how this leads to an interpretation of the Dirac field as a quantum field theory on Moyal-deformed Minkowski spacetime (with commutative time) in a setting of Lorentzian spectral geometries of which some basic aspects will be sketched. The scattering transformation will be shown to be unitarily implementable in the canonical vacuum representation of the Dirac field. Furthermore, it will be indicated how the functional derivatives of the ensuing unitary scattering operators with respect to the strength of the non-commutative potential induce, in the spirit of Bogoliubov's formula, quantum field operators (corresponding to observables) depending on the elements of the non-commutative algebra of Moyal-Minkowski spacetime.},
6739         archiveprefix = {arXiv},
6740         author = {M. Borris and R. Verch},
6741         doi = {10.1007/s00220-009-0905-2},
6742         eprint = {0812.0786},
6743         journal = {Commun. Math. Phys.},
6744         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Algebra (math.QA); kw:NC-Wick; kw:local-ncqft},
6745         localfile = {2008 - Borris, Verch - Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering.pdf},
6746         pages = {399--448},
6747         pdf = {http://arxiv.org/pdf/0812.0786},
6748         primaryclass = {math-ph},
6749         slaccitation = {\%\%CITATION = 0812.0786\\;\%\%},
6750         title = {{Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering}},
6751         url = {http://arxiv.org/abs/0812.0786},
6752         v1descr = {Wed, 3 Dec 2008 19:37:22 GMT (53kb)},
6753         volume = {293},
6754         year = {2010}
6755 }
6756 
6757 @book{Rieffel:1992,
6758         address = {Providence, Rhode Island},
6759         author = {M. A. Rieffel},
6760         keywords = {kw:NC-Wick},
6761         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Rieffel - Deformation Quantization for Actions of Rd.pdf},
6762         publisher = {American Mathematical Society},
6763         series = {{Memoirs of the Amerian Mathematical Society}},
6764         title = {{Deformation Quantization for Actions of $R^d$}},
6765         volume = {106},
6766         year = {1992}
6767 }
6768 
6769 @article{Rehren:1997,
6770         archiveprefix = {arXiv},
6771         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
6772         doi = {10.1023/A:1007368012557},
6773         eprint = {hep-th/9605156},
6774         journal = {Lett. Math. Phys.},
6775         localfile = {1997 - Rehren - Bounded Bose fields.pdf},
6776         pages = {299--306},
6777         slaccitation = {\%\%CITATION = HEP-TH/9605156\\;\%\%},
6778         title = {{Bounded Bose fields}},
6779         volume = {40},
6780         year = {1997}
6781 }
6782 
6783 @lecturenotes{Rehren:1997-1,
6784         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
6785         localfile = {1997 - Rehren - Konforme Quantenfeldtheorie.pdf; /home/gandalf/Physik/Lecture Notes/1997 - Rehren - Konforme Quantenfeldtheorie.pdf},
6786         school = {G\"{o}ttingen},
6787         title = {{Konforme Quantenfeldtheorie}},
6788         year = {1997}
6789 }
6790 
6791 @book{DiFrancescoMathieuSnchal:1997,
6792         author = {P. {Di Francesco} and P. Mathieu and D. S{\'{e}}n{\'{e}}chal},
6793         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Di Francesco P., Mathieu P., Senechal D. Conformal field theory (Springer 1997)(no preface)(K)(T)(908s)_PQft_.djvu},
6794         publisher = {Springer},
6795         title = {{Conformal Field Theory}},
6796         year = {1997}
6797 }
6798 
6799 @article{Bckenhauer:1996,
6800         abstract = {Based on the treatment of the chiral Ising model by Mack and Schomerus, we present examples of localized endomorphisms $\varrho_1^{loc}$ and $\varrho_{1/2}^{loc}$. It is shown that they lead to the same superselection sectors as the global ones in the sense that unitary equivalence $\pi_0\circ\varrho_1^{loc}\cong\pi_1$ and $\pi_0\circ\varrho_{1/2}^{loc}\cong\pi_{1/2}$ holds. Araki's formalism of the selfdual CAR algebra is used for the proof. We prove local normality and extend representations and localized endomorphisms to a global algebra of observables which is generated by local von Neumann algebras on the punctured circle. In this framework, we manifestly prove fusion rules and derive statistics operators.},
6801         archiveprefix = {arXiv},
6802         author = {J. B{\"{o}}ckenhauer},
6803         doi = {10.1007/BF02101894},
6804         eprint = {hep-th/9407079},
6805         journal = {Commun. Math. Phys.},
6806         localfile = {1996 - B\"{o}ckenhauer - Localized endomorphisms of the chiral Ising model.pdf},
6807         pages = {265--304},
6808         pdf = {http://arxiv.org/pdf/hep-th/9407079},
6809         slaccitation = {\%\%CITATION = HEP-TH/9407079\\;\%\%},
6810         title = {{Localized endomorphisms of the chiral Ising model}},
6811         url = {http://arxiv.org/abs/hep-th/9407079},
6812         volume = {177},
6813         year = {1996}
6814 }
6815 
6816 @lecturenotes{Fewster:2008,
6817         author = {C. J. Fewster},
6818         localfile = {2008 - Fewster - Lectures on quantum field theory in curved spacetime.pdf},
6819         school = {Leipzig},
6820         title = {{Lectures on quantum field theory in curved spacetime}},
6821         year = {2008}
6822 }
6823 
6824 @article{FurlanSotkovTodorov:1989,
6825         author = {P. Furlan and G. M. Sotkov and I. T. Todorov},
6826         journal = {Riv. del Nuovo Cimento},
6827         keywords = {Conformal Quantum Field Theory},
6828         localfile = {1988 - Furlan, Sotkov, Todorov - Two-dimensional conformal quantum field theory.pdf},
6829         number = {12},
6830         pages = {1--202},
6831         title = {{Two-Dimensional Conformal Quantum Field Theory}},
6832         volume = {6},
6833         year = {1989}
6834 }
6835 
6836 @article{LscherMack:1976,
6837         author = {M. L{\"{u}}scher and G. Mack},
6838         journal = {unpublished},
6839         title = {{The energy momentum tensor of critical quantum field theory in 1+1 dimensions}},
6840         year = {1976}
6841 }
6842 
6843 @article{KawahigashiLongo:2004,
6844         archiveprefix = {arXiv},
6845         author = {Y. Kawahigashi and R. Longo},
6846         eprint = {math-ph/0201015},
6847         journal = {Ann. Math.},
6848         keywords = {Algebraic Quantum Field Theory; Conformal Quantum Field Theory},
6849         localfile = {2004 - Kawahigashi, Longo - Classification of Local Conformal Nets. Case c < 1.pdf},
6850         pages = {493--522},
6851         slaccitation = {\%\%CITATION = MATH-PH/0201015\\;\%\%},
6852         title = {{Classification of local conformal nets: Case c $<$ 1}},
6853         volume = {160},
6854         year = {2004}
6855 }
6856 
6857 @article{McCoyTracyWu:1977,
6858         author = {B. M. McCoy and C. A. Tracy and T. T. Wu},
6859         doi = {10.1103/PhysRevLett.38.793},
6860         journal = {Phys. Rev. Lett.},
6861         localfile = {1977 - McCoy, Tracy, Wu - Two-Dimensional Ising Model as an Exactly Solvable Relativistic Quantum Field Theory: Explicit Formulas for n-Point Functions.pdf},
6862         pages = {793--796},
6863         slaccitation = {\%\%CITATION = PRLTA,38,793\\;\%\%},
6864         title = {{Two-Dimensional Ising Model as an Exactly Solvable Relativistic Quantum Field Theory: Explicit Formulas for n Point Functions}},
6865         volume = {38},
6866         year = {1977}
6867 }
6868 
6869 @article{Carpi:1999,
6870         author = {S. Carpi},
6871         doi = {10.1023/A:1007517131143},
6872         journal = {Lett. Math. Phys.},
6873         localfile = {1999 - Carpi - Classification of Subsystems for the Haag--Kastler Nets Generated by c = 1 Chiral Current Algebras.pdf},
6874         pages = {353--364},
6875         slaccitation = {\%\%CITATION = LMPHD,47,353\\;\%\%},
6876         title = {{Classification of subsystems for the Haag-Kastler nets generated by c = 1 chiral current algebras}},
6877         volume = {47},
6878         year = {1999}
6879 }
6880 
6881 @article{Carpi:1998,
6882         author = {S. Carpi},
6883         doi = {10.1023/A:1007466420114},
6884         journal = {Lett. Math. Phys.},
6885         localfile = {1998 - Carpi - Absence of Subsystems for the Haag--Kastler Net Generated by the Energy-Momentum Tensor in Two-Dimensional Conformal Field Theory.pdf},
6886         pages = {259--267},
6887         slaccitation = {\%\%CITATION = LMPHD,45,259\\;\%\%},
6888         title = {{Absence of subsystems for the Haag-Kastler net generated by the energy-momentum tensor in two-dimensional conformal field theory}},
6889         volume = {45},
6890         year = {1998}
6891 }
6892 
6893 @book{Heuser:1995,
6894         author = {H. Heuser},
6895         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Heuser H. Gewoehnliche Differentialgleichungen (Teubner, 1995)(de)(600dpi)(T)(628s)_MCde_.djvu},
6896         publisher = {Teubner},
6897         title = {{Gew\"{o}hnliche Differentialgleichungen}},
6898         year = {1995}
6899 }
6900 
6901 @article{Boller:2000,
6902         author = {S. Boller},
6903         journal = {Preprint},
6904         localfile = {2000 - Boller - Characterization of Cyclic and Separating Vectors and Application to an Inverse Problem in Modular Theory I. Finite Factors.pdf},
6905         title = {{Characterization of Cyclic and Separating Vectors and Application to an Inverse Problem in Modular Theory I. Finite Factors}},
6906         year = {2000}
6907 }
6908 
6909 @book{BaumgrtelWollenberg:1992,
6910         author = {H. Baumg{\"{a}}rtel and M. Wollenberg},
6911         localfile = {http://algebras.djvu},
6912         publisher = {Akademie Verlag},
6913         title = {{Causal Nets of Operator Algebras}},
6914         year = {1992}
6915 }
6916 
6917 @lecturenotes{Longo:2008,
6918         author = {R. Longo},
6919         localfile = {2008 - Longo - Lectures on Conformal Nets - part1.pdf},
6920         title = {{Lectures on Conformal Nets - Part 1}},
6921         year = {2008}
6922 }
6923 
6924 @lecturenotes{Longo:2008-1,
6925         author = {R. Longo},
6926         localfile = {2008 - Longo - Lectures on Conformal Nets - part2.pdf},
6927         title = {{Lectures on Conformal Nets - Part 2}},
6928         year = {2008}
6929 }
6930 
6931 @article{DtschFredenhagen:2001,
6932         author = {M. D{\"{u}}tsch and K. Fredenhagen},
6933         journal = {Preprint},
6934         localfile = {2001 - D\"{u}tsch, Fedenhagen - Perturbative Algebraic Field Theory, and Deformation Quantization.pdf},
6935         title = {{Perturbative Algebraic Field Theory, and Deformation Quantization}},
6936         year = {2001}
6937 }
6938 
6939 @mastersthesis{Ritz:2003,
6940         author = {E. Ritz},
6941         localfile = {2003 - Ritz - Normalit\"{a}tseigenschaften lokaler Gleichgewichtszust\"{a}nde in der relativistischen Quantenfeldtheorie.pdf},
6942         title = {{Normalit\"{a}tseigenschaften lokaler Gleichgewichtszust\"{a}nde in der relativistischen Quantenfeldtheorie}},
6943         year = {2003}
6944 }
6945 
6946 @article{BrunettiFredenhagenKhler:1996,
6947         abstract = {Quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis. We discuss a condition on the wave front set for the corresponding n-point distributions, called ``microlocal spectrum condition'' ($\mu$SC). On Minkowski space, this condition is satisfied as a consequence of the usual spectrum condition. Based on Radzikowski's determination of the wave front set of the two-point function of a free scalar field, satisfying the Hadamard condition in the Kay and Wald sense, we construct in the second part of this paper all Wick polynomials including the energy-momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our microlocal spectrum condition.},
6948         author = {R. Brunetti and K. Fredenhagen and M. K{\"{o}}hler},
6949         journal = {Commun. Math. Phys.},
6950         localfile = {1996 - Brunetti, Fredenhagen, K\"{o}hler - The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes.pdf},
6951         number = {180},
6952         pages = {633--652},
6953         title = {{The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes}},
6954         year = {1996}
6955 }
6956 
6957 @article{Hollands:2008,
6958         abstract = {In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are "associativity" or "factorization" conditions on the operator product expansion (OPE) of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.},
6959         archiveprefix = {arXiv},
6960         author = {S. Hollands},
6961         eprint = {0802.2198},
6962         localfile = {2008 - Hollands - Quantum field theory in terms of consistency conditions I: General framework, and perturbation theory via Hochschild cohomology.pdf},
6963         pdf = {http://arxiv.org/pdf/0802.2198},
6964         primaryclass = {hep-th},
6965         slaccitation = {\%\%CITATION = 0802.2198\\;\%\%},
6966         title = {{Quantum field theory in terms of consistency conditions I: General framework, and perturbation theory via Hochschild cohomology}},
6967         url = {http://arxiv.org/abs/0802.2198},
6968         year = {2008}
6969 }
6970 
6971 @article{Gerstenhaber:1964,
6972         author = {M. Gerstenhaber},
6973         journal = {Ann. Math.},
6974         keywords = {Mathematik},
6975         localfile = {1964 - Gerstenhaber - On the deformation of rings and algebras.pdf},
6976         pages = {59--103},
6977         title = {{On the deformation of rings and algebras}},
6978         url = {http://www.jstor.org/stable/1970484},
6979         volume = {79},
6980         year = {1964}
6981 }
6982 
6983 @misc{NahmKeegan:2009,
6984         abstract = {Integrable deformations of conformal field theories and the discrete Hirota equations.},
6985         author = {W. Nahm and S. Keegan},
6986         keywords = {High Energy Physics - Theory (hep-th)},
6987         localfile = {2009 - Nahm, Keegan - Integrable deformations of CFTs and the discrete Hirota equations.pdf},
6988         month = may,
6989         pdf = {http://arxiv.org/pdf/0905.3776},
6990         title = {{Integrable deformations of CFTs and the discrete Hirota equations}},
6991         url = {http://arxiv.org/abs/0905.3776},
6992         v1descr = {Sun, 24 May 2009 16:01:17 GMT (15kb)},
6993         year = {2009}
6994 }
6995 
6996 @article{GliozziTateo:1995,
6997         abstract = {We describe a new infinite family of multi-parameter functional equations for the Rogers dilogarithm, generalizing Abel's and Euler's formulas. They are suggested by the Thermodynamic Bethe Ansatz approach to the Renormalization Group flow of 2D integrable, ADE-related quantum field theories. The known sum rules for the central charge of critical fixed points can be obtained as special cases of these. We conjecture that similar functional identities can be constructed for any rational integrable quantum field theory with factorized S-matrix and support it with extensive numerical checks.},
6998         archiveprefix = {arXiv},
6999         author = {F. Gliozzi and R. Tateo},
7000         doi = {10.1016/0370-2693(95)00125-5},
7001         eprint = {hep-th/9411203},
7002         journal = {Phys. Lett.},
7003         localfile = {1995 - Gliozzi, Tateo - ADE functional dilogarithm identities and integrable models.pdf},
7004         pages = {84--88},
7005         pdf = {http://arxiv.org/pdf/hep-th/9411203},
7006         slaccitation = {\%\%CITATION = HEP-TH/9411203\\;\%\%},
7007         title = {{ADE functional dilogarithm identities and integrable models}},
7008         url = {http://arxiv.org/abs/hep-th/9411203},
7009         volume = {B348},
7010         year = {1995}
7011 }
7012 
7013 @book{GraciaBondiaVrillyFigueroa:2001,
7014         address = {Boston, Basel, Berlin},
7015         author = {J. M. Gracia-Bondia and J. C. V{\'{a}}rilly and H. Figueroa},
7016         isbn = {0817641246, 9780817641245},
7017         localfile = {http://geometry.djvu},
7018         publisher = {Birkh\"{a}user},
7019         series = {{Birkh\"{a}user Advanced Texts}},
7020         title = {{Elements of Noncommutative Geometry}},
7021         year = {2001}
7022 }
7023 
7024 @article{Weaver:1996,
7025         author = {N. Weaver},
7026         journal = {J. Oper. Theory},
7027         localfile = {1996 - Weaver - Deformations of von Neumann algebras.pdf},
7028         number = {2},
7029         pages = {223--239},
7030         title = {{Deformations of von Neumann algebras}},
7031         volume = {35},
7032         year = {1996}
7033 }
7034 
7035 @article{Rieffel:1981,
7036         author = {M. A. Rieffel},
7037         journal = {Math. Ann.},
7038         localfile = {1981 - Rieffel - Von Neumann algebras associated with pairs of lattices in Lie groups.pdf},
7039         pages = {403--418},
7040         title = {{Von Neumann Algebras Associated with Pairs of Lattices in Lie Groups }},
7041         volume = {257},
7042         year = {1981}
7043 }
7044 
7045 @article{Rieffel:1990-1,
7046         author = {M. A. Rieffel},
7047         journal = {Cont. Math.},
7048         localfile = {1990 - Rieffel - Non-commutative tori - a case study of non-commutative differentiable manifolds.pdf},
7049         pages = {191--121},
7050         title = {{Non-commutative tori - a case study of non-commutative differentiable manifolds}},
7051         volume = {105},
7052         year = {1990}
7053 }
7054 
7055 @misc{Schroer:2009-1,
7056         abstract = {It is shown that certain kinds of behavior which hitherto were expected to to be characteristic for classical and quantum gravity theory, as the infinite dimensional Bondi-Metzner-Sachs symmetry, holography on event horizons and an area proportionality of entropy, are in fact already present in QFT. In order to see this one has to leave the narrow framework of Lagangian quantization. It will be demonstrated that also the converse holds, namely QFT beyond the Lagrangian quantization setting receives crucial new impulses from the use of holographic projection onto horizons.},
7057         author = {B. Schroer},
7058         keywords = {High Energy Physics - Theory (hep-th)},
7059         localfile = {2009 - Schroer - BMS symmetry, holography on null-surfaces and area proportionality of light-slice entropy.pdf},
7060         month = may,
7061         pdf = {http://arxiv.org/pdf/0905.4435},
7062         title = {{BMS symmetry, holography on null-surfaces and area proportionality of light-slice entropy}},
7063         url = {http://arxiv.org/abs/0905.4435},
7064         v1descr = {Wed, 27 May 2009 16:31:16 GMT (32kb)},
7065         year = {2009}
7066 }
7067 
7068 @article{Lester:1984,
7069         author = {J. A. Lester},
7070         doi = {10.1063/1.526005},
7071         journal = {J. Math. Phys.},
7072         keywords = {cosmological models; lorentz transformations; minkowski space; transformations},
7073         localfile = {1982 - Lester - The causal automorphism of de Sitter and Einstein cylinder spacetimes.pdf},
7074         number = {1},
7075         pages = {113--116},
7076         title = {{The causal automorphism of de Sitter and Einstein cylinder spacetimes}},
7077         url = {http://link.aip.org/link/?JMP/25/113/1},
7078         volume = {25},
7079         year = {1984}
7080 }
7081 
7082 @article{vanSuijlekom:2004,
7083         abstract = {We present a new example of a finite-dimensional noncommutative manifold, namely the noncommutative cylinder. It is obtained by isospectral deformation of the canonical triple associated to the Euclidean cylinder. We discuss Connes' character formula for the cylinder. In the second part, we discuss noncommutative Lorentzian manifolds. Here, the definition of spectral triples involves Krein spaces and operators on Krein spaces. A central role is played by the admissible fundamental symmetries on the Krein space of square integrable sections of a spin bundle over a Lorentzian manifold. Finally, we discuss isospectral deformation of the Lorentzian cylinder and determine all admissible fundamental symmetries of the noncommutative cylinder.},
7084         author = {W.D. {van Suijlekom}},
7085         journal = {J.Math.Phys.},
7086         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
7087         localfile = {2003 - Suijlekom - The noncommutative Lorentzian cylinder as an isospectral deformation.pdf},
7088         pages = {537--556},
7089         pdf = {http://arxiv.org/pdf/math-ph/0310009},
7090         title = {{The noncommutative Lorentzian cylinder as an isospectral deformation}},
7091         url = {http://arxiv.org/abs/math-ph/0310009},
7092         v1descr = {Wed, 8 Oct 2003 15:03:17 GMT (23kb)},
7093         v1url = {http://www.arxiv.org/abs/math-ph/0310009v1},
7094         v2descr = {Wed, 15 Oct 2003 13:38:53 GMT (22kb)},
7095         volume = {45},
7096         year = {2004}
7097 }
7098 
7099 @article{CoburnXia:1995,
7100         author = {L.A. Coburn and J. Xia},
7101         doi = {10.1007/BF02099582},
7102         journal = {Commun. Math. Phys.},
7103         localfile = {1995 - Coburn, Xia - Toeplitz Algebras and Rieffel Deformations.pdf},
7104         number = {1},
7105         pages = {23--38},
7106         title = {{Toeplitz algebras and Rieffel deformations.}},
7107         volume = {168},
7108         year = {1995}
7109 }
7110 
7111 @misc{BieliavskyMaeda:2002,
7112         abstract = {We define non-tempered (exponential growth) function spaces on the Lie group ax+b which are stable under some left-invariant (convergent) star product.},
7113         author = {P. Bieliavsky and Y. Maeda},
7114         keywords = {kw:UDF; Mathematical Physics (math-ph); New-Deformations; Quantum Algebra (math.QA); Symplectic Geometry (math.SG)},
7115         localfile = {2002 - Bieliavsky, Maeda - Convergent Star Product Algebras on 'ax+b'.pdf},
7116         month = sep,
7117         pdf = {http://arxiv.org/pdf/math/0209295},
7118         title = {{Convergent star product algebras on 'ax+b'}},
7119         url = {http://arxiv.org/abs/math/0209295},
7120         v1descr = {Mon, 23 Sep 2002 12:25:42 GMT (9kb)},
7121         year = {2002}
7122 }
7123 
7124 @article{Bieliavsky:2002,
7125         abstract = {This work is a contribution to the area of Strict Quantization (in the sense of Rieffel) in the presence of curvature and non-Abelian group actions. More precisely, we use geometry to obtain explicit oscillatory integral formulae for strongly invariant strict deformation quantizations of a class of solvable symplectic symmetric spaces. Each of these quantizations gives rise to a field of (pre)-C*-algebras whose fibers are function algebras which are closed under the deformed product. The symmetry group of the symmetric space acts on each fiber by C*-algebra automorphisms.},
7126         author = {P. Bieliavsky},
7127         journal = {J. Symplectic Geom.},
7128         keywords = {Differential Geometry (math.DG); Mathematical Physics (math-ph); Quantum Algebra (math.QA); Symplectic Geometry (math.SG); kw:UDF},
7129         localfile = {2000 - Bieliavsky - Strict Quantization of Solvable Symmetric Spaces.pdf},
7130         month = oct,
7131         number = {2},
7132         pages = {269--320},
7133         pdf = {http://arxiv.org/pdf/math/0010004},
7134         title = {{Strict Quantization of Solvable Symmetric Spaces }},
7135         url = {http://arxiv.org/abs/math/0010004},
7136         v1descr = {Sun, 1 Oct 2000 14:46:34 GMT (36kb)},
7137         volume = {1},
7138         year = {2002}
7139 }
7140 
7141 @mastersthesis{Heller:2006,
7142         author = {J. G. Heller},
7143         keywords = {Deformation Quantization; kw:local-ncqft},
7144         localfile = {2006 - Heller - Lokal nichtkommutative Raumzeiten und Strikte Deformationsquantisierung - Diplom.pdf},
7145         note = {Diplomarbeit bei Stefan Waldmann},
7146         school = {Freiburg},
7147         title = {{Lokal nichtkommutative Raumzeiten und Strikte Deformationsquantisierung}},
7148         year = {2006}
7149 }
7150 
7151 @mastersthesis{Kaschek:2008,
7152         author = {D. Kaschek},
7153         keywords = {Deformation Quantization},
7154         localfile = {2008 - Kaschek - Nichtperturbative Deformationstheorie physikalischer Zust\"{a}nde - Diplomarbeit.pdf},
7155         note = {Diplomarbeit bei Stefan Waldmann},
7156         title = {{Nichtperturbative Deformationstheorie physikalischer Zust\"{a}nde}},
7157         year = {2008}
7158 }
7159 
7160 @book{Lance:1995,
7161         address = {Cambridge},
7162         author = {E.C. Lance},
7163         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Lance E.C. Hilbert C-Modules.. a toolkit for operator algebraists (CUP, 1995)(600dpi)(T)(ISBN 052147910X)(138s).djvu},
7164         publisher = {Cambridge University Press},
7165         title = {{Hilbert C*-Modules. A toolkit for operator algebraists}},
7166         year = {1995}
7167 }
7168 
7169 @article{FredenhagenHertel:1981,
7170         author = {K. Fredenhagen and J. Hertel},
7171         doi = {10.1007/BF01941663},
7172         journal = {Commun. Math. Phys.},
7173         localfile = {1981 - Fredenhagen, Hertel - Local algebras of observables and pointlike localized fields.pdf},
7174         pages = {555},
7175         slaccitation = {\%\%CITATION = CMPHA,80,555\\;\%\%},
7176         title = {{LOCAL ALGEBRAS OF OBSERVABLES AND POINT - LIKE LOCALIZED FIELDS}},
7177         volume = {80},
7178         year = {1981}
7179 }
7180 
7181 @book{Schiff:1999,
7182         author = {J. L. Schiff},
7183         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Schiff J.L. Laplace Transformation.. Theory and Applications (UTM, Springer,1999)(ISBN 0387986987)(245s)_MCat_.pdf},
7184         publisher = {Springer},
7185         title = {{Laplace Transformation - Theory and Applications}},
7186         year = {1999}
7187 }
7188 
7189 @article{Rivasseau:2009,
7190         abstract = {In this pedagogical note we propose to wander through five different methods to compute the number of connected graphs of the zero-dimensional $\phi^4$ field theory,in increasing order of sophistication. The note does not contain any new result but may be helpful to summarize the heart of constructive resummations, namely a replica trick and a forest formula.},
7191         author = {V. Rivasseau},
7192         journal = {Preprint},
7193         keywords = {Mathematical Physics (math-ph)},
7194         localfile = {2009 - Rivasseau - Constructive Field Theory in Zero Dimension.pdf},
7195         month = jun,
7196         pdf = {http://arxiv.org/pdf/0906.3524},
7197         title = {{Constructive Field Theory in Zero Dimension}},
7198         url = {http://arxiv.org/abs/0906.3524},
7199         v1descr = {Thu, 18 Jun 2009 20:25:47 GMT (26kb,D)},
7200         year = {2009}
7201 }
7202 
7203 @article{BrosBuchholz:1992,
7204         author = {J. Bros and D. Buchholz},
7205         doi = {10.1007/BF01565114},
7206         journal = {Z. Phys.},
7207         localfile = {1992 - Bros, Buchholz - Particles and propagators in relativistic thermo field theory.pdf},
7208         pages = {509--514},
7209         slaccitation = {\%\%CITATION = ZEPYA,C55,509\\;\%\%},
7210         title = {{Particles and propagators in relativistic thermo field theory}},
7211         volume = {C55},
7212         year = {1992}
7213 }
7214 
7215 @article{BrosBuchholz:1994,
7216         abstract = {It is shown that, under quite general conditions, thermal correlation functions in relativistic quantum field theory have stronger analyticity properties in configuration space than those imposed by the KMS-condition. These analyticity properties may be understood as a remnant of the relativistic spectrum condition in the vacuum sector and lead to a Lorentz-covariant formulation of the KMS-condition involving all space-time variables.},
7217         archiveprefix = {arXiv},
7218         author = {J. Bros and D. Buchholz},
7219         doi = {10.1016/0550-3213(94)00298-3},
7220         eprint = {hep-th/9807099},
7221         journal = {Nucl. Phys.},
7222         localfile = {1994 - Bros, Buchholz - Towards a Relativistic KMS Condition.pdf},
7223         pages = {291--318},
7224         pdf = {http://arxiv.org/pdf/hep-th/9807099},
7225         slaccitation = {\%\%CITATION = HEP-TH/9807099\\;\%\%},
7226         title = {{Towards a Relativistic KMS Condition}},
7227         url = {http://arxiv.org/abs/hep-th/9807099},
7228         volume = {B429},
7229         year = {1994}
7230 }
7231 
7232 @article{BrosBuchholz:1995,
7233         abstract = {A relativistic version of the Kubo--Martin--Schwinger boundary condition is presented which fixes the properties of thermal equilibrium states with respect to arbitrary space--time translations. This novel condition is a natural generalization of the relativistic spectrum condition in the vacuum theory and has similar consequences. In combination with the condition of locality it gives rise to a Kaellen--Lehmann type representation of thermal propagators with specific regularity properties. Possible applications of the results and some open problems are outlined.},
7234         archiveprefix = {arXiv},
7235         author = {J. Bros and D. Buchholz},
7236         eprint = {hep-th/9511022},
7237         localfile = {1995 - Bros, Buchholz - Relativistic KMS-condition and Kaellen-Lehmann type representatios of thermal propagators.pdf},
7238         pdf = {http://arxiv.org/pdf/hep-th/9511022},
7239         slaccitation = {\%\%CITATION = HEP-TH/9511022\\;\%\%},
7240         title = {{Relativistic KMS-condition and Kaellen-Lehmann type representatios of thermal propagators}},
7241         url = {http://arxiv.org/abs/hep-th/9511022},
7242         year = {1995}
7243 }
7244 
7245 @article{BrosBuchholz:1996,
7246         abstract = {We provide an axiomatic framework for Quantum Field Theory at finite temperature which implies the existence of general analyticity properties of the $ n $-point functions; the latter parallel the properties derived from the usual Wightman axioms in the vacuum representation of Quantum Field Theory. Complete results are given for the propagators, including a generalization of the K\"{a}ll\'{e}n-Lehmann representation. Some known examples of ``hard-thermal-loop calculations'' and the representation of ``quasiparticles'' are discussed in this general framework.},
7247         archiveprefix = {arXiv},
7248         author = {J. Bros and D. Buchholz},
7249         eprint = {hep-th/9606046},
7250         journal = {Ann. Poincare},
7251         localfile = {1996 - Bros, Buchholz - Axiomatic analyticity properties and representations of particles in thermal quantum field theory.pdf},
7252         pages = {495--522},
7253         pdf = {http://arxiv.org/pdf/hep-th/9606046},
7254         slaccitation = {\%\%CITATION = HEP-TH/9606046\\;\%\%},
7255         title = {{Axiomatic analyticity properties and representations of particles in thermal quantum field theory}},
7256         url = {http://arxiv.org/abs/hep-th/9606046},
7257         volume = {64},
7258         year = {1996}
7259 }
7260 
7261 @article{BrosBuchholz:1998,
7262         abstract = {The problem of extracting the modes of Goldstone bosons from a thermal background is reconsidered in the framework of relativistic quantum field theory. It is shown that in the case of spontaneous breakdown of an internal bosonic symmetry a recently established decomposition of thermal correlation functions contains certain specific contributions which can be attributed to a particle of zero mass.},
7263         archiveprefix = {arXiv},
7264         author = {J. Bros and D. Buchholz},
7265         doi = {10.1103/PhysRevD.58.125012},
7266         eprint = {hep-th/9608139},
7267         journal = {Phys. Rev.},
7268         localfile = {1998 - Bros, Buchholz - The unmasking of thermal Goldstone bosons.pdf},
7269         pages = {125012},
7270         pdf = {http://arxiv.org/pdf/hep-th/9608139},
7271         slaccitation = {\%\%CITATION = HEP-TH/9608139\\;\%\%},
7272         title = {{The unmasking of thermal Goldstone bosons}},
7273         url = {http://arxiv.org/abs/hep-th/9608139},
7274         volume = {D58},
7275         year = {1998}
7276 }
7277 
7278 @article{BrosBuchholz:2002,
7279         abstract = {It is shown that the timelike asymptotic properties of thermal correlation functions in relativistic quantum field theory can consistently be described in terms of free fields carrying some stochastic degree of freedom which couples to the thermal background. These ``asymptotic thermal fields'' have specific algebraic properties (commutation relations) and their dynamics can be expressed in terms of asymptotic field equations. The formalism is applied to interacting theories where it yields concrete non-perturbative results for the asymptotic thermal propagators. The results are consistent with the expected features of dissipative propagation of the constitutents of thermal states, outlined in previous work, and they shed new light on the non-perturbative effects of thermal backgrounds.},
7280         archiveprefix = {arXiv},
7281         author = {J. Bros and D. Buchholz},
7282         doi = {10.1016/S0550-3213(02)00059-7},
7283         eprint = {hep-ph/0109136},
7284         journal = {Nucl. Phys.},
7285         localfile = {2002 - Bros, Buchholz - Asymptotic dynamics of thermal quantum fields.pdf},
7286         pages = {289--310},
7287         pdf = {http://arxiv.org/pdf/hep-ph/0109136},
7288         slaccitation = {\%\%CITATION = HEP-PH/0109136\\;\%\%},
7289         title = {{Asymptotic dynamics of thermal quantum fields}},
7290         url = {http://arxiv.org/abs/hep-ph/0109136},
7291         volume = {B627},
7292         year = {2002}
7293 }
7294 
7295 @article{Jaekel:1998,
7296         abstract = {The basic ingredients of Tomita-Takesaki modular theory are used to establish cluster estimates. Applications to thermal quantum field theory are discussed.},
7297         archiveprefix = {arXiv},
7298         author = {C. D. J{\"{a}}kel},
7299         eprint = {hep-th/9804017},
7300         localfile = {1999 - J\"{a}kel - Cluster Estimates for Modular Structures.pdf},
7301         pdf = {http://arxiv.org/pdf/hep-th/9804017},
7302         slaccitation = {\%\%CITATION = HEP-TH/9804017\\;\%\%},
7303         title = {{Cluster estimates for modular structures}},
7304         url = {http://arxiv.org/abs/hep-th/9804017},
7305         year = {1998}
7306 }
7307 
7308 @article{Rieffel:1993,
7309         author = {M. A. Rieffel},
7310         journal = {Cont. Math.},
7311         localfile = {1993 - Rieffel - Compact quantum groups associated with toral subgroups.pdf},
7312         title = {{Compact quantum groups associated with toral subgroups}},
7313         url = {http://www.math.berkeley.edu/~rieffel/papers/compact.pdf},
7314         volume = {145},
7315         year = {1993}
7316 }
7317 
7318 @article{Rieffel:1995,
7319         author = {M. A. Rieffel},
7320         journal = {Commun. Math. Phys.},
7321         localfile = {1995 - Rieffel - Non-compact quantum groups associated with abelian subgroups.pdf},
7322         pages = {181--201},
7323         title = {{Non-compact quantum groups associated with abelian subgroups}},
7324         volume = {171},
7325         year = {1995}
7326 }
7327 
7328 @article{Rieffel:1974,
7329         author = {M. A. Rieffel},
7330         journal = {Adv. Math.},
7331         localfile = {1974 - Rieffel - Induced Representations of C-Algebras.pdf},
7332         pages = {176--257},
7333         title = {{Induced representations of C*-algebras}},
7334         volume = {13},
7335         year = {1974}
7336 }
7337 
7338 @article{AkoforBalachandran:2009,
7339         abstract = {In this paper, we initiate the study of finite temperature quantum field theories (QFT's) on the Moyal plane. Such theories violate causality which influences the properties of these theories. In particular, causality influences the fluctuation-dissipation theorem: as we show, a disturbance in a space-time region $M\_1$ creates a response in a space-time region $M\_2$ space-like with respect to $M\_1$ ($M\_1\times M\_2$). The relativistic Kubo formula with and without noncommutativity is discussed in detail, and the modified properties of relaxation time and the dependence of mean square fluctuations on time are derived. In particular, the Sinha-Sorkin result \cite{sorkin-sinha} on the logarithmic time dependence of the mean square fluctuations is discussed in our context. We derive an exact formula for the noncommutative susceptibility in terms of the susceptibility for the corresponding commutative case. It shows that noncommutative corrections in the four-momentum space have remarkable periodicity properties as a function of the four-momentum $k$. They have direction dependence as well and vanish for certain directions of the spatial momentum. These are striking observable signals for noncommutativity. The Lehmann representation is also generalized to any value of the noncommutativity parameter $\theta^{\mu\nu}$ and finite temperatures.},
7340         author = {E. Akofor and A. P. Balachandran},
7341         journal = {Phys. Rev. D},
7342         keywords = {High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech)},
7343         localfile = {2009 - Akofor, Balachandran - Finite Temperature Field Theory on the Moyal Plane.pdf},
7344         number = {SU-4252-885},
7345         pages = {036008},
7346         pdf = {http://arxiv.org/pdf/0907.0905},
7347         title = {{Finite Temperature Field Theory on the Moyal Plane}},
7348         url = {http://arxiv.org/abs/0907.0905},
7349         v1descr = {Mon, 6 Jul 2009 17:08:58 GMT (14kb)},
7350         volume = {80},
7351         year = {2009}
7352 }
7353 
7354 @article{BertrandBertrand:1998,
7355         abstract = {The study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f\&gt;0 with linear operators defined on the positive-frequency signals. Full attention is given to its construction which is entirely based on the study of the affine group in a simple and direct way. The correspondence rule is detailed and the associated Wigner function is given. Formulas expressing the basic operation (star-bracket) of the Lie algebra of symbols, which is isomorphic to that of the operators, are obtained. In addition, it is shown that the resulting calculus is covariant under a three-parameter group which contains the affine group as subgroup. This observation is the starting point of an investigation leading to a whole class of symbolic calculi which can be considered as modifications of the original one.},
7356         archiveprefix = {arXiv},
7357         author = {J. Bertrand and P. Bertrand},
7358         doi = {10.1063/1.532484},
7359         eprint = {physics/9708027},
7360         journal = {J. Math. Phys.},
7361         localfile = {1998 - Bertrand, Bertrand - Symbolic calculus on the time-frequency half-plane.pdf},
7362         pages = {4071--4090},
7363         pdf = {http://arxiv.org/pdf/physics/9708027},
7364         slaccitation = {\%\%CITATION = PHYSICS/9708027\\;\%\%},
7365         title = {{Symbolic calculus on the time frequency half plane}},
7366         url = {http://arxiv.org/abs/physics/9708027},
7367         volume = {39},
7368         year = {1998}
7369 }
7370 
7371 @article{KarowskiKurakSchroer:1979,
7372         author = {M. Karowski and V. Kurak and B. Schroer},
7373         doi = {10.1016/0370-2693(79)90523-9},
7374         journal = {Phys. Lett.},
7375         localfile = {1978 - Karowski, Kurak, Schroer - Confinement in two-dimensional models with factorization.pdf},
7376         pages = {200},
7377         slaccitation = {\%\%CITATION = PHLTA,B81,200\\;\%\%},
7378         title = {{Confinement in two-dimensional models with factorization}},
7379         volume = {B81},
7380         year = {1979}
7381 }
7382 
7383 @mastersthesis{Quella:1999,
7384         author = {T. Quella},
7385         keywords = {Form Factor Program},
7386         localfile = {1999 - Quella - Formfaktoren und Lokalit\"{a}t in integrablen Modellen der Quantenfeldtheorie in 1+1 Dimensionen.pdf},
7387         school = {FU Berlin},
7388         title = {{Formfaktoren und Lokalit\"{a}t in integrablen Modellen der Quantenfeldtheorie in 1+1 Dimensionen}},
7389         year = {1999}
7390 }
7391 
7392 @article{GalluccioLizziVitale:2009,
7393         abstract = {We show that the Ultraviolet/Infrared mixing of noncommutative field theories with the Gronewold-Moyal product, whereby some (but not all) ultraviolet divergences become infrared, is a generic feature of translationally invariant associative products. We find, with an explicit calculation that the phase appearing in the nonplanar diagrams is the one given by the commutator of the coordinates, the semiclassical Poisson structure of the non commutative spacetime. We do this with an explicit calculation for represented generic products.},
7394         author = {S. Galluccio and Fedele Lizzi and P. Vitale},
7395         journal = {JHEP},
7396         keywords = {High Energy Physics - Theory (hep-th)},
7397         localfile = {2009 - Galluccio, Lizzi, Vitale - Translation Invariance, Commutation Relations and Ultraviolet-Infrared Mixing.pdf},
7398         month = jul,
7399         pages = {054},
7400         pdf = {http://arxiv.org/pdf/0907.3640},
7401         title = {{Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing}},
7402         url = {http://arxiv.org/abs/0907.3640},
7403         v1descr = {Tue, 21 Jul 2009 13:05:42 GMT (27kb)},
7404         volume = {0909},
7405         year = {2009}
7406 }
7407 
7408 @book{Arnold:1978,
7409         author = {V.I. Arnold},
7410         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Arnold V.I. Ordinary differential equations (MIT, 1978)(no TOC)(400dpi)(T)(273s).djvu},
7411         publisher = {MIT},
7412         title = {{Ordinary differential equations}},
7413         year = {1978}
7414 }
7415 
7416 @book{Teschl:2004,
7417         author = {G. Teschl},
7418         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Teschl G. Ordinary differential equations (lecture notes, web draft, 2004)(243s).pdf},
7419         title = {{Ordinary Differential Equations and Dynamical Systems}},
7420         volume = {Lecture Notes (Web draft)},
7421         year = {2004}
7422 }
7423 
7424 @book{Chicone:1999,
7425         author = {C. Chicone},
7426         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Chicone C. Ordinary Differential Equations with Applications(TAM 34,Springer,1999)(ISBN 0387985352)(571s)_MCde_.pdf},
7427         publisher = {Springer},
7428         series = {{Texts in Applied Mathematics}},
7429         title = {{Ordinary Differential Equations with Applications}},
7430         volume = {34},
7431         year = {1999}
7432 }
7433 
7434 @article{VarillyGraciaBondia:1989,
7435         author = {J. C. Varilly and J. M. Gracia-Bondia},
7436         doi = {10.1016/0003-4916(89)90262-5},
7437         journal = {Annals Phys.},
7438         localfile = {1989 - Varilly, Gracia-Bondia - The Moyal Representation for Spin.pdf},
7439         pages = {107--148},
7440         slaccitation = {\%\%CITATION = APNYA,190,107\\;\%\%},
7441         title = {{The Moyal representation for spin}},
7442         volume = {190},
7443         year = {1989}
7444 }
7445 
7446 @book{Williams:2007,
7447         address = {Providence, Rhode Island},
7448         author = {D. P. Williams},
7449         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Williams - Crossed products of C-algebras.djvu},
7450         publisher = {American Mathematical Society},
7451         title = {{Crossed products of C*-algebras}},
7452         year = {2007}
7453 }
7454 
7455 @article{Bahns:2009,
7456         abstract = {It is shown that the $n$-point functions of scalar massive free fields on the noncommutative Minkowski space are distributions which are boundary values of analytic functions. Contrary to what one might expect, this construction does not provide a connection to the popular traditional Euclidean approach to noncommutative field theory (unless the time variable is assumed to commute). Instead, one finds Schwinger functions with twistings involving only momenta that are on the mass-shell. This explains why renormalization in the traditional Euclidean noncommutative framework crudely differs from renormalization in the Minkowskian regime.},
7457         author = {D. Bahns},
7458         journal = {Annales Henri Poincare},
7459         keywords = {High Energy Physics - Theory (hep-th); kw:NC-Wick; Mathematical Physics (math-ph)},
7460         localfile = {2009 - Bahns - Schwinger functions in noncommutative quantum field theory.pdf},
7461         pages = {1273--1283},
7462         pdf = {http://arxiv.org/pdf/0908.4537},
7463         title = {{Schwinger functions in noncommutative quantum field theory}},
7464         url = {http://arxiv.org/abs/0908.4537},
7465         v1descr = {Mon, 31 Aug 2009 14:02:09 GMT (23kb)},
7466         volume = {11},
7467         year = {2010}
7468 }
7469 
7470 @misc{Schroer:2009-2,
7471         abstract = {It is often overlooked that local quantum physics has a built in quantum localization structure which may under certain circumstances disagree with (differential, algebraic) geometric ideas. String theory originated from such a spectacular misinterpretation of a source-target embedding in which an inner symmetry of the source object becomes the Lorentz symmetry of the target space. The quantum localization reveals however that the resulting object is an infinite component pointlike field. There are also other other areas in QFT which suffered from having followed geometrical metaphors and payed too little attention to the autonomous localization properties. This will be illustrated in the concrete context of three examples. We also show that "modular localization ", i.e. the intrinsic localization theory of local quantum quantum physics, leads to a radiacal new way of looking at (nonperturbative) QFT. For the first time in the history of QFT there are now existence theorems for a class of strictly renormalizable (i.e. not superrenormalizable) factorizable QFTs which are based on these new concepts. The paper ends with some worrisome sociological observations about the state of particle physics and the direction in which it is heading. These remarks are based on the results presented in the three previous sections.},
7472         author = {B. Schroer},
7473         keywords = {General Physics (physics.gen-ph)},
7474         localfile = {2009 - Schroer - Geometry and Localization, a metaphorically related pair.pdf},
7475         month = jun,
7476         pdf = {http://arxiv.org/pdf/0906.2067},
7477         title = {{Geometry and Localization, a metaphorically related pair}},
7478         url = {http://arxiv.org/abs/0906.2067},
7479         v1descr = {Thu, 11 Jun 2009 15:08:32 GMT (12kb)},
7480         v1url = {http://www.arxiv.org/abs/0906.2067v1},
7481         v2descr = {Mon, 22 Jun 2009 16:40:34 GMT (24kb)},
7482         v2url = {http://www.arxiv.org/abs/0906.2067v2},
7483         v3descr = {Tue, 23 Jun 2009 17:19:29 GMT (25kb)},
7484         year = {2009}
7485 }
7486 
7487 @book{Jaenich:1999,
7488         author = {K. J{\"{a}}nich},
7489         edition = {5},
7490         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Jaenich K. Funktionentheorie (5ed., Springer, 1999)(de)(L)(T)(ISBN 3540661522)(66s).djvu},
7491         publisher = {Springer},
7492         title = {{Funktionentheorie - Eine Einf\"{u}hrung}},
7493         year = {1999}
7494 }
7495 
7496 @misc{BrunettiFredenhagenHoge:2009,
7497         abstract = {In the Schroedinger equation, time plays a special role as an external parameter. We show that in an enlarged system where the time variable denotes an additional degree of freedom, solutions of the Schroedinger equation give rise to weights on the enlarged algebra of observables. States in the associated GNS representation correspond to states on the original algebra composed with a completely positive unit preserving map. Application of this map to the functions of the time operator on the large system delivers the positive operator valued maps which were previously proposed by two of us as time observables. As an example we discuss the application of this formalism to the Wheeler-DeWitt theory of a scalar field on a Robertson-Walker spacetime.},
7498         author = {R. Brunetti and K. Fredenhagen and M. Hoge},
7499         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)},
7500         localfile = {2009 - Brunetti, Fredenhagen, Hoge - Time in quantum physics: From an external parameter to an intrinsic observable.pdf},
7501         month = sep,
7502         pdf = {http://arxiv.org/pdf/0909.1899},
7503         title = {{Time in quantum physics: From an external parameter to an intrinsic observable}},
7504         url = {http://arxiv.org/abs/0909.1899},
7505         v1descr = {Thu, 10 Sep 2009 09:46:39 GMT (10kb)},
7506         year = {2009}
7507 }
7508 
7509 @book{Folland:1989,
7510         author = {G.B. Folland},
7511         localfile = {http://space.djvu},
7512         publisher = {Princeton University Press},
7513         series = {{Annals of Mathematics Studies}},
7514         title = {{Harmonic Analysis in Phase Space}},
7515         year = {1989}
7516 }
7517 
7518 @misc{DabrowskiPiacitelli:2009,
7519         abstract = {Starting from a discussion of the concrete representations of the coordinates of the k-Minkowski spacetime (in 1+1 dimensions, for simplicity), we explicitly compute the associated Weyl operators as functions of a pair of Schroedinger operators. This allows for explicitly computing the trace of a quantised function of spacetime. Moreover, we show that in the classical (i.e. large scale) limit the origin of space is a topologically isolated point, so that the resulting classical spacetime is disconnected. Finally we show that there exist states with arbitrarily sharp simultaneous localisation in all the coordinates; in other words, an arbitrarily high energy density can be transferred to spacetime by means of localisation alone, which amounts to say that the model is not stable under localisation.},
7520         author = {L. Dabrowski and G. Piacitelli},
7521         keywords = {High Energy Physics - Theory (hep-th)},
7522         localfile = {2009 - Dabrowski, Piacitelli - The k-Minkowski Spacetime: Trace, Classical Limit and uncertainty Relations.pdf},
7523         month = sep,
7524         pdf = {http://arxiv.org/pdf/0909.3215},
7525         title = {{The k-Minkowski Spacetime: Trace, Classical Limit and uncertainty Relations}},
7526         url = {http://arxiv.org/abs/0909.3215},
7527         v1descr = {Thu, 17 Sep 2009 14:24:52 GMT (9kb)},
7528         year = {2009}
7529 }
7530 
7531 @article{FredenhagenRehrenSeiler:2007,
7532         abstract = {We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum gravity and string theory.},
7533         archiveprefix = {arXiv},
7534         author = {K. Fredenhagen and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren and E. Seiler},
7535         doi = {10.1007/978-3-540-71117-9_4},
7536         eprint = {hep-th/0603155},
7537         journal = {Lect. Notes Phys.},
7538         localfile = {2006 - Fredenhagen, Rehren, Seiler - Quantum Field Theory: Where We Are.pdf},
7539         pages = {61--87},
7540         pdf = {http://arxiv.org/pdf/hep-th/0603155},
7541         slaccitation = {\%\%CITATION = HEP-TH/0603155\\;\%\%},
7542         title = {{Quantum Field Theory: Where We Are}},
7543         url = {http://arxiv.org/abs/hep-th/0603155},
7544         volume = {721},
7545         year = {2007}
7546 }
7547 
7548 @book{ConnesCuntzGuentnerHigsonKaminkerRoberts:2000,
7549         author = {A. Connes and J. Cuntz and E. Guentner and N. Higson and J. Kaminker and J. E. Roberts},
7550         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Connes A., Cuntz J., et al., Noncommutative geometry, CIME lectures, 2000, LNM1831, Springer, 2004, 359s.pdf},
7551         publisher = {Springer},
7552         series = {{Lecture Notes in Mathematics}},
7553         title = {{Noncommutative Geometry}},
7554         year = {2000}
7555 }
7556 
7557 @article{Mueger:1998,
7558         author = {M. M{\"{u}}ger},
7559         journal = {Communications in Mathematical Physics},
7560         localfile = {1998 - M\"{u}ger - Quantum Double Actions on Operator Algebras and Orbifold Quantum Field Theories.pdf},
7561         number = {1},
7562         pages = {137--181},
7563         publisher = {Springer},
7564         title = {{Quantum double actions on operator algebras and orbifold quantum field theories}},
7565         volume = {191},
7566         year = {1998}
7567 }
7568 
7569 @article{AlbeverioMotovilov:2005,
7570         author = {S. Albeverio and A.K. Motovilov},
7571         journal = {Preprint},
7572         localfile = {2005 - Albeverio, Motovilov - Operator integrals with respect to a spectral measure and solutions to some operator equations.pdf},
7573         title = {{Operator integrals with respect to a spectral measure and solutions to some operator equations}},
7574         year = {2005}
7575 }
7576 
7577 @book{Pedersen:1979,
7578         author = {G.K. Pedersen},
7579         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Pedersen G.K. C-algebras and their authomorphism groups (AP, 1979)(600dpi)(T)(ISBN 0125494505)(426s).djvu},
7580         publisher = {Academic Press},
7581         title = {{C*-Algebras and their Automorphism Groups}},
7582         year = {1979}
7583 }
7584 
7585 @article{Moschella:2005,
7586         author = {U. Moschella},
7587         journal = {Seminaire Poincare},
7588         localfile = {2005 - Moschella - The de Sitter and anti-de Sitter sightseeing tour.pdf},
7589         number = {1},
7590         pages = {1--12},
7591         title = {{The de Sitter and anti-de Sitter Sightseeing Tour}},
7592         year = {2005}
7593 }
7594 
7595 @article{BuchholzLechnerSummers:2010,
7596         abstract = {Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations of C*-dynamical systems with automorphic actions of R^n, whenever the latter are presented in a covariant representation. Moreover, the device can be used for the deformation of relativistic quantum field theories by adjusting the convolutions to the geometry of Minkowski space. The resulting deformed theories still comply with pertinent physical principles and their Tomita-Takesaki modular data coincide with those of the undeformed theory; but they are in general inequivalent to the undeformed theory and exhibit different physical interpretations.},
7597         author = {D. Buchholz and G. Lechner and S. J. Summers},
7598         doi = {10.1007/s00220-010-1137-1},
7599         journal = {Commun. Math. Phys.},
7600         keywords = {kw:NC-Wick; kw:warping; Mathematical Physics (math-ph); Operator Algebras (math.OA); Quantum Physics (quant-ph)},
7601         localfile = {2010 - Buchholz, Lechner, Summers - Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories.pdf},
7602         pages = {95--123},
7603         pdf = {http://arxiv.org/pdf/1005.2656},
7604         title = {{Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories}},
7605         url = {http://arxiv.org/abs/1005.2656},
7606         v1descr = {Sat, 15 May 2010 08:35:06 GMT (33kb)},
7607         volume = {304},
7608         x-color = {#199bff},
7609         year = {2011}
7610 }
7611 
7612 @article{DappiaggiLechnerMorfaMorales:2010,
7613         abstract = {The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes. These spacetimes carry a family of wedge-like regions which share the essential causal properties of the Poincare transforms of the Rindler wedge in Minkowski space. In the setting of deformed quantum field theories, they play the role of typical localization regions of quantum fields and observables. As a concrete example of such a procedure, the deformation of the free Dirac field is studied.},
7614         author = {C. Dappiaggi and G. Lechner and E. Morfa-Morales},
7615         doi = {10.1007/s00220-011-1210-4},
7616         journal = {Commun. Math. Phys.},
7617         keywords = {kw:warping},
7618         localfile = {2010 - Dappiaggi, Lechner, Morfa-Morales - Deformations of quantum field theories on spacetimes with Killing fields.pdf},
7619         number = {1},
7620         pages = {99--130},
7621         title = {{Deformations of quantum field theories on spacetimes with Killing fields}},
7622         url = {http://arxiv.org/abs/1006.3548},
7623         volume = {305},
7624         x-color = {#199bff},
7625         year = {2011}
7626 }
7627 
7628 @article{Lechner:2009-1,
7629         author = {G. Lechner},
7630         journal = {Proceedings of the ICMP 2009, Prague},
7631         localfile = {2009 - Lechner - Deformations of Operator Algebras and the Construction of Quantum Field Theories.pdf},
7632         title = {{Deformations of Operator Algebras and the Construction of Quantum Field Theories}},
7633         x-color = {#199bff},
7634         year = {2009}
7635 }
7636 
7637 @article{Doplicher:2009,
7638         author = {S. Doplicher},
7639         journal = {Prerint},
7640         localfile = {2009 - Doplicher - The Principle of Locality. Effectiveness, fate and challenges.pdf},
7641         title = {{The Principle of Locality. Effectiveness, fate and challenges}},
7642         url = {http://arxiv.org/abs/0911.5136},
7643         year = {2009}
7644 }
7645 
7646 @book{Waldmann:2007,
7647         author = {S. Waldmann},
7648         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Waldmann - Poisson-Geometrie und Deformationsquantisierung.pdf},
7649         publisher = {Springer},
7650         title = {{Poisson-Geometrie und Deformationsquantisierung}},
7651         year = {2007}
7652 }
7653 
7654 @article{DappiaggiMorettiPinamonti:2009,
7655         author = {C. Dappiaggi and V. Moretti and N. Pinamonti},
7656         journal = {Commun. Math. Phys.},
7657         localfile = {2007 - Dappiaggi, Moretti, Pinamonti - Cosmological horizons and reconstruction of quantum field theories.pdf},
7658         pages = {1129},
7659         title = {{Cosmological horizons the reconstruciton of quantum field theories}},
7660         url = {http://arxiv.org/abs/0712.1770},
7661         volume = {285},
7662         year = {2009}
7663 }
7664 
7665 @article{DappiaggiMorettiPinamonti:2009-1,
7666         author = {C. Dappiaggi and V. Moretti and N. Pinamonti},
7667         journal = {J. Math. Phys.},
7668         localfile = {2008 - Dappiaggi, Moretti, Pinamonti - Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property.pdf},
7669         pages = {062304},
7670         title = {{Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property}},
7671         volume = {50},
7672         year = {2009}
7673 }
7674 
7675 @article{Manchak:2009,
7676         author = {J.B. Manchak},
7677         journal = {Gen. Relativ. Gravit.},
7678         localfile = {2009 - Manchak - Is spacetime hole free.pdf},
7679         number = {7},
7680         pages = {1639--1643},
7681         publisher = {Springer},
7682         title = {{Is spacetime hole-free?}},
7683         volume = {41},
7684         year = {2009}
7685 }
7686 
7687 @article{Kuckert:2000,
7688         author = {B. Kuckert},
7689         journal = {Commun. Math. Phys.},
7690         localfile = {2000 - Kuckert - Localization Regions of Local Observables.pdf},
7691         number = {1},
7692         pages = {197--216},
7693         publisher = {Springer},
7694         title = {{Localization regions of local observables}},
7695         volume = {215},
7696         year = {2000}
7697 }
7698 
7699 @article{Masiello:1994,
7700         author = {A. Masiello},
7701         localfile = {1994 - Masiello - Convex regions of Lorentzian manifolds.pdf},
7702         title = {{Convex regions of Lorentzian manifolds}},
7703         year = {1994}
7704 }
7705 
7706 @article{CagnacheDAndreaMartinettiWallet:2009,
7707         author = {E. Cagnache and F. D'Andrea and P. Martinetti and {{{{{{{{{{{{{{{{{{{{{{{{{J.-C.}}}}}}}}}}}}}}}}}}}}}}}}} Wallet},
7708         journal = {Preprint},
7709         localfile = {2009 - Cagnache, D'Andrea, Martinetti, Wallet - The spectral distance on the Moyal plane.pdf},
7710         title = {{The spectral distance on the Moyal plane}},
7711         url = {http://arxiv.org/abs/0912.0906},
7712         year = {2009}
7713 }
7714 
7715 @article{LongoMartinettiRehren:2009,
7716         author = {R. Longo and P. Martinetti and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
7717         journal = {Preprint},
7718         keywords = {CGMA},
7719         localfile = {2009 - Longo, Martinetti, Rehren - Geometric modular action for disjoint intervals and boundary conformal field theory.pdf},
7720         title = {{Geometric modular action for disjoint intervals and boundary conformal field theory}},
7721         url = {http://arxiv.org/abs/0912.1106},
7722         year = {2009}
7723 }
7724 
7725 @article{SahlmannVerch:2000,
7726         author = {H. Sahlmann and R. Verch},
7727         journal = {Commun. Math. Phys.},
7728         localfile = {2000 - Sahlmann, Verch - Passivity and microlocal spectrum condition.pdf},
7729         number = {3},
7730         pages = {705--731},
7731         publisher = {Springer},
7732         title = {{Passivity and microlocal spectrum condition}},
7733         url = {http://arxiv.org/abs/math-ph/0002021},
7734         volume = {214},
7735         year = {2000}
7736 }
7737 
7738 @article{BorchersBuchholz:1999,
7739         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and D. Buchholz},
7740         journal = {Annales Poincare Phys. Theor.},
7741         localfile = {1999 - Borchers, Buchholz - Global properties of vacuum states in de Sitter space.pdf},
7742         pages = {23--40},
7743         title = {{Global properties of vacuum states in de Sitter space}},
7744         url = {http://arxiv.org/abs/gr-qc/9803036},
7745         volume = {A70},
7746         year = {1999}
7747 }
7748 
7749 @book{Wald:1984,
7750         author = {R. M. Wald},
7751         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Wald R.M. General relativity (1984)(T)(ISBN 0226870332)(494s).djvu},
7752         publisher = {University of Chicago Press},
7753         title = {{General Relativity}},
7754         year = {1984}
7755 }
7756 
7757 @article{Borchers:2009,
7758         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
7759         journal = {Preprint},
7760         localfile = {2009 - Borchers - On the Net of von Neumann algebras associated with a Wedge and Wedge-causal Manifolds.pdf},
7761         title = {{On the Net of von Neumann algebras associated with a Wedge and Wedge-causal Manifolds}},
7762         url = {http://www.lqp.uni-goe.de/papers/09/12/09120802.html},
7763         year = {2009}
7764 }
7765 
7766 @phdthesis{Claessens:2007,
7767         author = {L. Claessens},
7768         localfile = {2009 - Claessens - Locally anti de Sitter spaces and deformation quantization.pdf},
7769         school = {Louvain},
7770         title = {{Locally anti de Sitter spaces and deformation quantization}},
7771         year = {2007}
7772 }
7773 
7774 @article{OhlSchenkel:2009,
7775         author = {T. Ohl and A. Schenkel},
7776         journal = {Preprint},
7777         localfile = {2009 - Ohl, Schenkel - Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes.pdf},
7778         title = {{Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes}},
7779         url = {http://arxiv.org/abs/0912.2252},
7780         year = {2009}
7781 }
7782 
7783 @book{SachsWu:1977,
7784         author = {R.K. Sachs and H. Wu},
7785         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Sachs R.K., Wu H. General relativity for mathematicians (Springer, 1977)(T)(ISBN 038790218X)(301s).djvu},
7786         publisher = {Springer},
7787         title = {{General relativity for mathematicians}},
7788         year = {1977}
7789 }
7790 
7791 @misc{Streater:2010,
7792         abstract = {So far only quasifree fields have been shown to satisfy the Haag-Araki axioms for local algebras of observables; we show from a model in 1 + 1 dimensions that there can be representations in which two ingoing free particles produce a pair of out-going solitons with positive probability, which can be computed. This happens when the experiment is designed to observe this outcome. It is proposed that the same idea will work in four dimensions.},
7793         author = {R. F. Streater},
7794         keywords = {High Energy Physics - Theory (hep-th)},
7795         localfile = {2010 - Streater - A Scattering Theory based on Free Fields.pdf},
7796         month = jan,
7797         pdf = {http://arxiv.org/pdf/1001.1882},
7798         title = {{A Scattering Theory Based on Free Fields}},
7799         url = {http://arxiv.org/abs/1001.1882},
7800         v1descr = {Tue, 12 Jan 2010 13:41:20 GMT (10kb)},
7801         year = {2010}
7802 }
7803 
7804 @book{Sakai:1971,
7805         author = {S. Sakai},
7806         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Sakai S. C-star-algebras and W-star-algebras (Springer, 1971)(600dpi)(T)(270s).djvu},
7807         publisher = {Springer},
7808         title = {{C*-Algebras and W*-Algebras}},
7809         year = {1971}
7810 }
7811 
7812 @book{Arveson:1976,
7813         author = {W. Arveson},
7814         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Arveson W. An invitation to C-algebras (Springer, 1976)(600dpi)(T)(116s).djvu},
7815         publisher = {Springer},
7816         title = {{An Invitation to C*-Algebras}},
7817         year = {1976}
7818 }
7819 
7820 @article{ArakiWoods:1966,
7821         author = {H. Araki and J. Woods},
7822         journal = {Publ. RIMS, Kyoto University},
7823         localfile = {1966 - Araki, Woods - Complete Boolean algebras of type I factors.pdf},
7824         pages = {157--242},
7825         title = {{Complete Boolean algebras of type I factors}},
7826         volume = {A2},
7827         year = {1966}
7828 }
7829 
7830 @book{Guichardet:1972,
7831         author = {A. Guichardet},
7832         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Guichardet. Symmetric Hilbert Spaces and Related Topics (LNM0261, Springer, 1972)(ISBN 3540058036)(T)(202s).djvu},
7833         publisher = {Springer},
7834         title = {{Symmetric Hilbert Spaces and Related Topics}},
7835         year = {1972}
7836 }
7837 
7838 @misc{LangvikZahabi:2010,
7839         abstract = {We consider various modifications of the Weyl-Moyal star-product, in order to obtain a finite range of nonlocality. The basic requirements are to preserve the commutation relations of the coordinates as well as the associativity of the new product. We show that a modification of the differential representation of the Weyl-Moyal star-product by an exponential function of derivatives will not lead to a finite range of nonlocality. We also modify the integral kernel of the star-product introducing a Gaussian damping, but find a nonassociative product which remains infinitely nonlocal. We are therefore led to propose that the Weyl-Moyal product should be modified by a cutoff like function, in order to remove the infinite nonlocality of the product. We provide such a product, but it appears that one has to abandon the possibility of analytic calculation with the new product.},
7840         author = {M. L{\aa}ngvik and A. Zahabi},
7841         keywords = {High Energy Physics - Theory (hep-th)},
7842         localfile = {2010 - L{\aa}ngvik, Zahabi - On Finite Noncommutativity in Quantum Field Theory.pdf},
7843         month = feb,
7844         pdf = {http://arxiv.org/pdf/1002.0956},
7845         title = {{On Finite Noncommutativity in Quantum Field Theory}},
7846         url = {http://arxiv.org/abs/1002.0956},
7847         v1descr = {Thu, 4 Feb 2010 12:44:06 GMT (15kb)},
7848         year = {2010}
7849 }
7850 
7851 @phdthesis{Porrmann:2000,
7852         abstract = {The concept of particle weights has been introduced by Buchholz and the author in order to obtain a unified treatment of particles as well as (charged) infraparticles which do not permit a definition of mass and spin according to Wigner's theory. Particle weights arise as temporal limits of physical states in the vacuum sector and describe the asymptotic particle content. Following a thorough analysis of the underlying notion of localizing operators, we give a precise definition of this concept and investigate the characteristic properties. The decomposition of particle weights into pure components which are linked to irreducible representations of the quasi-local algebra has been a long-standing desideratum that only recently found its solution. We set out two approaches to this problem by way of disintegration theory, making use of a physically motivated assumption concerning the structure of phase space in quantum field theory. The significance of the pure particle weights ensuing from this disintegration is founded on the fact that they exhibit features of improper energy-momentum eigenstates, analogous to Dirac's conception, and permit a consistent definition of mass and spin even in an infraparticle situation.},
7853         author = {M. Porrmann},
7854         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
7855         localfile = {2000 - Porrmann - The Concept of Particle Weights in Local Quantum Field Theory - PhD-Thesis.pdf},
7856         month = may,
7857         pdf = {http://arxiv.org/pdf/hep-th/0005057},
7858         title = {{The Concept of Particle Weights in Local Quantum Field Theory}},
7859         url = {http://arxiv.org/abs/hep-th/0005057},
7860         v1descr = {Sat, 6 May 2000 13:30:57 GMT (123kb)},
7861         year = {2000}
7862 }
7863 
7864 @phdthesis{Sanders:2008,
7865         abstract = {This thesis considers various aspects of locally covariant quantum field theory (LCQFT; see Brunetti et al., Commun.Math.Phys. 237 (2003), 31-68), a mathematical framework to describe axiomatic quantum field theories in curved spacetimes. New results include: a philosophical interpretation of certain aspects of this framework in terms of modal logic; a proof that the truncated n-point functions of any Hadamard state of the free real scalar field are smooth, except for n=2; a description of he free Dirac field in a representation independent way, showing that the theory is determined entirely by the relations between the adjoint map, the charge conjugation map and the Dirac operator; a proof that the relative Cauchy evolution of the free Dirac field is related to its stress-energy-momentum tensor in the same way as for the free real scalar field (cf. loc.cit.); several results on the Reeh-Schlieder property in LCQFT, including but not limited to those of our earlier paper; a new and elegant approach to wave front sets of Banach space-valued distributions, which allows easy proofs and extensions of results in the literature.},
7866         author = {K. Sanders},
7867         keywords = {Mathematical Physics (math-ph)},
7868         localfile = {2008 - Sanders - Aspects of locally covariant quantum field theory - PhD-Thesis.pdf},
7869         month = sep,
7870         pdf = {http://arxiv.org/pdf/0809.4828},
7871         school = {University of York},
7872         title = {{Aspects of locally covariant quantum field theory}},
7873         url = {http://arxiv.org/abs/0809.4828},
7874         v1descr = {Sun, 28 Sep 2008 08:45:31 GMT (117kb,D)},
7875         year = {2008}
7876 }
7877 
7878 @misc{Sanders:2009,
7879         abstract = {We prove that the singularity structure of all n-point distributions of a state of a generalised real free scalar field in curved spacetime can be estimated if the two-point distribution is of Hadamard form. In particular this applies to the real free scalar field and the result has applications in perturbative quantum field theory, showing that the class of all Hadamard states is the state space of interest. In our proof we assume that the field is a generalised free field, i.e. that it satisies scalar (c-number) commutation relations, but it need not satisfy an equation of motion. The same argument also works for anti-commutation relations and it can be generalised to vector-valued fields. To indicate the strengths and limitations of our assumption we also prove the analogues of a theorem by Borchers and Zimmermann on the self-adjointness of field operators and of a very weak form of the Jost-Schroer theorem. The original proofs of these results in the Wightman framework make use of analytic continuation arguments. In our case no analyticity is assumed, but to some extent the scalar commutation relations can take its place.},
7880         author = {K. Sanders},
7881         keywords = {Mathematical Physics (math-ph)},
7882         localfile = {2009 - Sanders - Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime.pdf},
7883         month = mar,
7884         pdf = {http://arxiv.org/pdf/0903.1021},
7885         title = {{Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime}},
7886         url = {http://arxiv.org/abs/0903.1021},
7887         v1descr = {Thu, 5 Mar 2009 15:33:03 GMT (19kb)},
7888         year = {2009}
7889 }
7890 
7891 @article{Sanders:2009-1,
7892         abstract = {We attempt to prove the existence of Reeh-Schlieder states on curved spacetimes in the framework of locally covariant quantum field theory using the idea of spacetime deformation and assuming the existence of a Reeh-Schlieder state on a diffeomorphic (but not isometric) spacetime. We find that physically interesting states with a weak form of the Reeh-Schlieder property always exist and indicate their usefulness. Algebraic states satisfying the full Reeh-Schlieder property also exist, but are not guaranteed to be of physical interest.},
7893         author = {K. Sanders},
7894         journal = {Commun. Math. Phys.},
7895         keywords = {Mathematical Physics (math-ph)},
7896         localfile = {2008 - Sanders - On the Reeh-Schlieder Property in Curved Spacetime.pdf},
7897         pages = {271--285},
7898         pdf = {http://arxiv.org/pdf/0801.4676},
7899         title = {{On the Reeh-Schlieder Property in Curved Spacetime}},
7900         url = {http://arxiv.org/abs/0801.4676},
7901         v1descr = {Wed, 30 Jan 2008 14:01:50 GMT (18kb)},
7902         volume = {288},
7903         year = {2009}
7904 }
7905 
7906 @techreport{DappiaggiPinamontiPorrmann:2010,
7907         abstract = {In the framework of the algebraic formulation, we discuss and analyse some new features of the local structure of a real scalar quantum field theory in a strongly causal spacetime. In particular we use the properties of the exponential map to set up a local version of a bulk-to-boundary correspondence. The bulk is a suitable subset of a geodesic neighbourhood of any but fixed point p of the underlying background, while the boundary is a part of the future light cone having p as its own tip. In this regime, we provide a novel notion for the extended *-algebra of Wick polynomials on the said cone and, on the one hand, we prove that it contains the information of the bulk counterpart via an injective *-homomorphism while, on the other hand, we associate to it a distinguished state whose pull-back in the bulk is of Hadamard form. The main advantage of this point of view arises if one uses the universal properties of the exponential map and of the light cone in order to show that, for any two given backgrounds M and M' and for any two subsets of geodesic neighbourhoods of two arbitrary points, it is possible to engineer the above procedure such that the boundary extended algebras are related via a restriction homomorphism. This allows for the pull-back of boundary states in both spacetimes and, thus, to set up a machinery which permits the comparison of expectation values of local field observables in M and M'.},
7908         author = {C. Dappiaggi and N. Pinamonti and M. Porrmann},
7909         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
7910         localfile = {2010 - Dappiaggi, Pinamonti, Porrmann - Local causal structures, Hadamard states and the principle of local covariance in quantum field theory.pdf},
7911         month = jan,
7912         number = {Desy 10-001, ESI 2203, ZMP-HH/09-33},
7913         pdf = {http://arxiv.org/pdf/1001.0858},
7914         title = {{Local causal structures, Hadamard states and the principle of local covariance in quantum field theory}},
7915         url = {http://arxiv.org/abs/1001.0858},
7916         v1descr = {Wed, 6 Jan 2010 11:07:03 GMT (45kb)},
7917         year = {2010}
7918 }
7919 
7920 @article{Pinamonti:2009,
7921         abstract = {In this paper we generalize the construction of generally covariant quantum theories given in the work of Brunetti, Fredenhagen and Verch to encompass the conformal covariant case. After introducing the abstract framework, we discuss the massless conformally coupled Klein Gordon field theory, showing that its quantization corresponds to a functor between two certain categories. At the abstract level, the ordinary fields, could be thought as natural transformations in the sense of category theory. We show that, the Wick monomials without derivatives (Wick powers), can be interpreted as fields in this generalized sense, provided a non trivial choice of the renormalization constants is given. A careful analysis shows that the transformation law of Wick powers is characterized by a weight, and it turns out that the sum of fields with different weights breaks the conformal covariance. At this point there is a difference between the previously given picture due to the presence of a bigger group of covariance. It is furthermore shown that the construction does not depend upon the scale mu appearing in the Hadamard parametrix, used to regularize the fields. Finally, we briefly discuss some further examples of more involved fields.},
7922         author = {N. Pinamonti},
7923         doi = {10.1007/s00220-009-0780-x},
7924         journal = {Commun. Math. Phys.},
7925         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
7926         localfile = {2008 - Pinamonti - Conformal generally covariant quantum field theory: The scalar field and its Wick products.pdf},
7927         pages = {1117--1135},
7928         pdf = {http://arxiv.org/pdf/0806.0803},
7929         title = {{Conformal generally covariant quantum field theory: The scalar field and its Wick products}},
7930         url = {http://arxiv.org/abs/0806.0803},
7931         v1descr = {Wed, 4 Jun 2008 15:24:27 GMT (19kb)},
7932         v1url = {http://www.arxiv.org/abs/0806.0803v1},
7933         v2descr = {Tue, 3 Feb 2009 09:34:30 GMT (22kb)},
7934         volume = {288},
7935         year = {2009}
7936 }
7937 
7938 @lecturenotes{Waldmann:2009,
7939         author = {S. Waldmann},
7940         localfile = {2009 - Waldmann - Geometric Wave Equations.pdf},
7941         title = {{Geometric Wave Equations}},
7942         year = {2009}
7943 }
7944 
7945 @phdthesis{LauridsenRibeiro:2007,
7946         author = {P. Lauridsen-Ribeiro},
7947         localfile = {2007 - Lauridsen-Ribeiro - Structural and Dynamical Aspects of the AdS-CFT Correspondence - a Rigorous Approach - PhD-Thesis.pdf},
7948         school = {Sao Paulo},
7949         title = {{Structural and Dynamical Aspects of the AdS/CFT Correspondence: a Rigorous Approach}},
7950         url = {http://arxiv.org/abs/0712.0401},
7951         year = {2007}
7952 }
7953 
7954 @book{Jaenich:1993,
7955         author = {K. J{\"{a}}nich},
7956         edition = {2},
7957         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Jaenich K. Vektoranalysis (2ed., Springer, 1993)(de)(L)(T)(ISBN 3540571426)(143s).djvu},
7958         publisher = {Springer},
7959         title = {{Vektoranalysis}},
7960         year = {1993}
7961 }
7962 
7963 @book{Isham:2001,
7964         author = {C. J. Isham},
7965         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Isham C.J. Modern Differential Geometry for Physicists (WS, 2001)(T)(306s).djvu},
7966         publisher = {World Scientific},
7967         title = {{Modern Differential Geometry for Physicists}},
7968         year = {2001}
7969 }
7970 
7971 @book{Janich:1999,
7972         author = {K. J{\"{a}}nich},
7973         edition = {6},
7974         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/J\"{a}nich - Topologie.djvu},
7975         publisher = {Springer},
7976         title = {{Topologie}},
7977         year = {1999}
7978 }
7979 
7980 @book{Rudin:1991,
7981         author = {W. Rudin},
7982         edition = {2},
7983         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Rudin - Functional Analysis.djvu},
7984         publisher = {McGraw-Hill},
7985         title = {{Functional Analysis}},
7986         year = {1991}
7987 }
7988 
7989 @misc{Longo:2000,
7990         abstract = {Recent applications of Operator Algebras to Quantum Field Theory on a Curved Spacetime show that the incremental entropy associated with a quantum black hole, due the addition of a short range charge, is quantized proportionally to the logarithm of an integer. This talk first reviews the case of a Rindler black hole and then sketches the case of a spacetime with bifurcate Killing horizon and charges localizable on the horizon. An important tool is the construction of the conformal symmetries on the horizon.},
7991         author = {R. Longo},
7992         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
7993         localfile = {2000 - Longo - The Bisognano-Wichmann Theorem for Charged States and the Conformal Boundary of a Black Hole.pdf},
7994         month = jan,
7995         pdf = {http://arxiv.org/pdf/math-ph/0001034},
7996         title = {{The Bisognano-Wichmann Theorem for Charged States and the Conformal Boundary of a Black Hole}},
7997         url = {http://arxiv.org/abs/math-ph/0001034},
7998         v1descr = {Fri, 21 Jan 2000 19:40:21 GMT (8kb)},
7999         year = {2000}
8000 }
8001 
8002 @book{GalindoPascual:1990,
8003         author = {A. Galindo and P. Pascual},
8004         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Galindo A., Pascual P. Quantum mechanics I (Springer, 1990)(ISBN 0387514066)(T) (431s).djvu},
8005         publisher = {Springer},
8006         title = {{Quantum Mechanics I}},
8007         year = {1990}
8008 }
8009 
8010 @book{GalindoPascual:1991,
8011         author = {A. Galindo and P. Pascual},
8012         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Galindo A., Pascual P. Quantum mechanics II (Springer, 1991)(ISBN 038752309X)(T)(388s).djvu},
8013         publisher = {Springer},
8014         title = {{Quantum Mechanics II}},
8015         year = {1991}
8016 }
8017 
8018 @book{O'Neill:1983,
8019         author = {B. O'Neill},
8020         localfile = {http://geometry.djvu},
8021         publisher = {Academic Press},
8022         title = {{Semi-Riemannian Geometry}},
8023         year = {1983}
8024 }
8025 
8026 @book{Jost:2005,
8027         author = {J. Jost},
8028         localfile = {http://analysis.djvu},
8029         publisher = {Springer},
8030         title = {{Postmodern Analysis}},
8031         year = {2005}
8032 }
8033 
8034 @book{AbdallaAbdallaRothe:1991,
8035         author = {E. Abdalla and C. Abdalla and K.D. Rothe},
8036         localfile = {http://qft.djvu},
8037         publisher = {World Scientific},
8038         title = {{Non-perturbative methods in 2-dimensional quantum field theory}},
8039         year = {1991}
8040 }
8041 
8042 @article{BernalSanchez:2005,
8043         abstract = {The folk questions in Lorentzian Geometry, which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime $(M,g)$ admits a smooth time function $\tau$ whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting $M= \R \times {\cal S}$, $g= - \beta(\tau,x) d\tau^2 + \bar g\_\tau $, (b) if a spacetime $M$ admits a (continuous) time function $t$ (i.e., it is stably causal) then it admits a smooth (time) function $\tau$ with timelike gradient $\nabla \tau$ on all $M$.},
8044         author = {A. N. Bernal and M. S{\'{a}}nchez},
8045         doi = {10.1007/s00220-005-1346-1},
8046         journal = {Commun. Math. Phys.},
8047         keywords = {Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc)},
8048         localfile = {2005 - Bernal, Sanchez - Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes.pdf},
8049         pages = {43--50},
8050         pdf = {http://arxiv.org/pdf/gr-qc/0401112},
8051         title = {{Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes}},
8052         url = {http://arxiv.org/abs/gr-qc/0401112},
8053         v1descr = {Wed, 28 Jan 2004 16:38:07 GMT (9kb)},
8054         v1url = {http://www.arxiv.org/abs/gr-qc/0401112v1},
8055         v2descr = {Thu, 4 Nov 2004 11:20:09 GMT (9kb)},
8056         v2url = {http://www.arxiv.org/abs/gr-qc/0401112v2},
8057         v3descr = {Tue, 15 Feb 2005 18:45:19 GMT (10kb)},
8058         volume = {257},
8059         year = {2005}
8060 }
8061 
8062 @article{BernalSanchez:2006,
8063         abstract = {Recently, folk questions on the smoothability of Cauchy hypersurfaces and time functions of a globally hyperbolic spacetime M, have been solved. Here we give further results, applicable to several problems: (1) Any compact spacelike acausal submanifold H with boundary can be extended to a spacelike Cauchy hypersurface S. If H were only achronal, counterexamples to the smooth extension exist, but a continuous extension (in fact, valid for any compact achronal subset K) is still possible. (2) Given any spacelike Cauchy hypersurface S, a Cauchy temporal function T (i.e., a smooth function with past-directed timelike gradient everywhere, and Cauchy hypersurfaces as levels) with S equal to one of the levels, is constructed -thus, the spacetime splits orthogonally as $R \times S$ in a canonical way. Even more, accurate versions of this result are obtained if the Cauchy hypersurface S were non-spacelike (including non-smooth, or achronal but non-acausal).},
8064         author = {A. N. Bernal and M. S{\'{a}}nchez},
8065         doi = {10.1007/s11005-006-0091-5},
8066         journal = {Lett.Math.Phys.},
8067         keywords = {Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc)},
8068         localfile = {2006 - Bernal, Sanchez - Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions.pdf},
8069         pages = {183--197},
8070         pdf = {http://arxiv.org/pdf/gr-qc/0512095},
8071         title = {{Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions}},
8072         url = {http://arxiv.org/abs/gr-qc/0512095},
8073         v1descr = {Thu, 15 Dec 2005 18:57:39 GMT (180kb)},
8074         volume = {77},
8075         year = {2006}
8076 }
8077 
8078 @book{SeifertThrelfall:1980,
8079         author = {H. Seifert and W. Threlfall},
8080         localfile = {http://topology.djvu},
8081         publisher = {Academic Press},
8082         title = {{A Textbook of Topology}},
8083         year = {1980}
8084 }
8085 
8086 @book{Chandrasekhar:1983,
8087         author = {S. Chandrasekhar},
8088         localfile = {http://holes.djvu},
8089         publisher = {Oxford University Press},
8090         title = {{The mathematical theory of black holes}},
8091         year = {1983}
8092 }
8093 
8094 @article{ChandrasekharFerrari:1984,
8095         author = {S. Chandrasekhar and V. Ferrari},
8096         journal = {Proc. Roy. Soc. Lond.},
8097         pages = {55},
8098         slaccitation = {\%\%CITATION = PRSLA,A396,55\\;\%\%},
8099         title = {{On the Nutku-Halil solution for colliding impulsive gravitational waves}},
8100         volume = {A396},
8101         year = {1984}
8102 }
8103 
8104 @article{Ellis:2006,
8105         author = {G. F. R. Ellis},
8106         doi = {10.1007/s10714-006-0283-4},
8107         journal = {Gen. Rel. Grav.},
8108         localfile = {2006 - Ellis - The Bianchi Models - Then and Now.pdf},
8109         pages = {1003--1015},
8110         slaccitation = {\%\%CITATION = GRGVA,38,1003\\;\%\%},
8111         title = {{The Bianchi models: Then and now}},
8112         volume = {38},
8113         year = {2006}
8114 }
8115 
8116 @article{FullingParkerHu:1974,
8117         author = {S. A. Fulling and L. Parker and B. L. Hu},
8118         doi = {10.1103/PhysRevD.10.3905},
8119         journal = {Phys. Rev.},
8120         pages = {3905--3924},
8121         slaccitation = {\%\%CITATION = PHRVA,D10,3905\\;\%\%},
8122         title = {{Conformal energy-momentum tensor in curved spacetime: Adiabatic regularization and renormalization}},
8123         volume = {D10},
8124         year = {1974}
8125 }
8126 
8127 @book{BarGinouxPfaffle:2007,
8128         author = {C. B{\"{a}}r and N. Ginoux and F. Pf{\"{a}}ffle},
8129         publisher = {European Mathematical Society},
8130         title = {{Wave Equations on Lorentzian Manifolds and Quantization}},
8131         year = {2007}
8132 }
8133 
8134 @book{Wald:1994,
8135         author = {R. M. Wald},
8136         localfile = {http://thermodynamics.djvu},
8137         publisher = {Chicago University Press},
8138         title = {{Quantum field theory in curved space-time and black hole thermodynamics}},
8139         year = {1994}
8140 }
8141 
8142 @article{Radzikowski:1996,
8143         author = {M. J. Radzikowski},
8144         doi = {10.1007/BF02101180},
8145         journal = {Commun. Math. Phys.},
8146         pages = {1--22},
8147         slaccitation = {\%\%CITATION = CMPHA,180,1\\;\%\%},
8148         title = {{A Local to global singularity theorem for quantum field theory on curved space-time}},
8149         volume = {180},
8150         year = {1996}
8151 }
8152 
8153 @article{Radzikowski:1996-1,
8154         author = {M. J. Radzikowski},
8155         doi = {10.1007/BF02100096},
8156         journal = {Commun. Math. Phys.},
8157         pages = {529--553},
8158         slaccitation = {\%\%CITATION = CMPHA,179,529\\;\%\%},
8159         title = {{Micro-local approach to the Hadamard condition in quantum field theory on curved space-time}},
8160         volume = {179},
8161         year = {1996}
8162 }
8163 
8164 @article{AllenFolacci:1987,
8165         author = {B. Allen and A. Folacci},
8166         doi = {10.1103/PhysRevD.35.3771},
8167         journal = {Phys. Rev.},
8168         pages = {3771},
8169         slaccitation = {\%\%CITATION = PHRVA,D35,3771\\;\%\%},
8170         title = {{The massless minimally coupled scalar field in de Sitter space}},
8171         volume = {D35},
8172         year = {1987}
8173 }
8174 
8175 @article{Geroch:1968,
8176         author = {R. P. Geroch},
8177         doi = {10.1063/1.1664507},
8178         journal = {J. Math. Phys.},
8179         pages = {1739--1744},
8180         slaccitation = {\%\%CITATION = JMAPA,9,1739\\;\%\%},
8181         title = {{Spinor structure of space-times in general relativity. I}},
8182         volume = {9},
8183         year = {1968}
8184 }
8185 
8186 @article{Geroch:1970,
8187         author = {R. P. Geroch},
8188         doi = {10.1063/1.1665067},
8189         journal = {J. Math. Phys.},
8190         pages = {343--348},
8191         slaccitation = {\%\%CITATION = JMAPA,11,343\\;\%\%},
8192         title = {{Spinor structure of space-times in general relativity. II}},
8193         volume = {11},
8194         year = {1970}
8195 }
8196 
8197 @book{HawkingEllis:1973,
8198         author = {S. Hawking and G. F. R. Ellis},
8199         localfile = {http://spacetime.djvu},
8200         publisher = {Cambridge University Press},
8201         title = {{The large scale structure of space-time}},
8202         year = {1973}
8203 }
8204 
8205 @book{Higham:,
8206         author = {N. J. Higham},
8207         localfile = {http://sciences.djvu},
8208         publisher = {SIAM},
8209         title = {{Handbook of Writing for the Mathematical Sciences}},
8210         year = {1998}
8211 }
8212 
8213 @article{Rehren:2000,
8214         abstract = {A rigorous (and simple) proof is given that there is a one-to-one correspondence between causal anti-deSitter covariant quantum field theories on anti-deSitter space and causal conformally covariant quantum field theories on its conformal boundary. The correspondence is given by the explicit identification of observables localized in wedge regions in anti-deSitter space and observables localized in double-cone regions in its boundary. It takes vacuum states into vacuum states, and positive-energy representations into positive-energy representations.},
8215         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
8216         journal = {Annales Henri Poincare},
8217         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
8218         localfile = {1999 - Rehren - Algebraic Holography.pdf},
8219         pages = {607--623},
8220         pdf = {http://arxiv.org/pdf/hep-th/9905179},
8221         title = {{Algebraic Holography}},
8222         url = {http://arxiv.org/abs/hep-th/9905179},
8223         v1descr = {Tue, 25 May 1999 13:32:37 GMT (21kb)},
8224         v1url = {http://www.arxiv.org/abs/hep-th/9905179v1},
8225         v2descr = {Tue, 1 Jun 1999 09:10:35 GMT (22kb)},
8226         v2url = {http://www.arxiv.org/abs/hep-th/9905179v2},
8227         v3descr = {Tue, 10 Aug 1999 12:11:45 GMT (25kb)},
8228         v3url = {http://www.arxiv.org/abs/hep-th/9905179v3},
8229         v4descr = {Thu, 7 Oct 1999 12:18:56 GMT (26kb)},
8230         volume = {1},
8231         year = {2000}
8232 }
8233 
8234 @article{Keyl:1996,
8235         author = {M. Keyl},
8236         doi = {10.1142/S0129055X96000093},
8237         journal = {Rev. Math. Phys.},
8238         pages = {229--270},
8239         slaccitation = {\%\%CITATION = RMPHE,8,229\\;\%\%},
8240         title = {{Causal spaces, causal complements and their relations to quantum field theory}},
8241         volume = {8},
8242         year = {1996}
8243 }
8244 
8245 @article{Buchholz:2000,
8246         archiveprefix = {arXiv},
8247         author = {D. Buchholz},
8248         eprint = {math-ph/0011044},
8249         journal = {Preprint},
8250         localfile = {2000 - Buchholz - Algebraic quantum field theory: A Status report.pdf},
8251         slaccitation = {\%\%CITATION = MATH-PH/0011044\\;\%\%},
8252         title = {{Algebraic quantum field theory: A status report}},
8253         year = {2000}
8254 }
8255 
8256 @article{Kay:1985,
8257         author = {B. S. Kay},
8258         doi = {10.1007/BF01212687},
8259         journal = {Commun. Math. Phys.},
8260         localfile = {1985 - Kay - The double-wedge algebra for quantum fields on Schwarzschild and Minkowski spacetimes.pdf},
8261         pages = {57},
8262         slaccitation = {\%\%CITATION = CMPHA,100,57\\;\%\%},
8263         title = {{The double-wedge algebra for quantum fields on Schwarzschild and Minkowski space-times}},
8264         url = {http://projecteuclid.org/euclid.cmp/1103943337},
8265         volume = {100},
8266         year = {1985}
8267 }
8268 
8269 @article{Bieliavsky:2007,
8270         abstract = {We define a universal deformation formula (UDF) for the actions of the affine group on Frechet algebras. More precisely, starting with any associative Frechet algebra which the affine group acts on in a strongly continuous and isometrical manner, the UDF produces a family of topological associative algebra structures on the space of smooth vectors of the action deforming the initial product. The deformation field obtained is based over an infinite dimensional parameter space naturally associated with the space of pseudo-differential operators on the real line. This note also presents some geometrical aspects of the UDF and in particular its relation with hyperbolic geometry.},
8271         author = {P. Bieliavsky},
8272         journal = {Preprint},
8273         keywords = {Operator Algebras (math.OA); Quantum Algebra (math.QA); kw:UDF},
8274         localfile = {2007 - Bieliavsky - Deformation quantization for actions of the affine group.pdf},
8275         month = sep,
8276         pdf = {http://arxiv.org/pdf/0709.1110},
8277         title = {{Deformation quantization for actions of the affine group }},
8278         url = {http://arxiv.org/abs/0709.1110},
8279         v1descr = {Fri, 7 Sep 2007 16:27:31 GMT (19kb)},
8280         year = {2007}
8281 }
8282 
8283 @article{BieliavskyDetournayRoomanSpindel:2004,
8284         abstract = {space-time admits a foliation by two-dimensional twisted conjugacy classes, stable under the identification subgroup yielding the non-rotating massive BTZ black hole. Each leaf constitutes a classical solution of the space-time Dirac-Born-Infeld action, describing an open D-string in $AdS\_3$ or a D-string winding around the black hole. We first describe two nonequivalent maximal extensions of the non-rotating massive BTZ space-time and observe that in one of them, each D-string worldsheet admits an action of a two-parameter subgroup ($AdS\_3$) of $\cn$. We then construct non-formal, $\SL$-invariant, star products that deform the classical algebra of functions on the D-string worldsheets and on their embedding space-times. We end by giving the first elements towards the definition of a Connes spectral triple on non-commutative $\cn$ space-times.$AdS$},
8285         author = {P. Bieliavsky and S. Detournay and M. Rooman and P. Spindel},
8286         journal = {JHEP},
8287         keywords = {High Energy Physics - Theory (hep-th); kw:UDF},
8288         localfile = {2004 - Bieliavsky, Detournay, Rooman, Spindel - Star products on extended massive non-rotating BTZ black holes.pdf},
8289         pages = {031},
8290         pdf = {http://arxiv.org/pdf/hep-th/0403257},
8291         title = {{Star products on extended massive non-rotating BTZ black holes}},
8292         url = {http://arxiv.org/abs/hep-th/0403257},
8293         v1descr = {Thu, 25 Mar 2004 18:06:41 GMT (289kb)},
8294         volume = {0406},
8295         year = {2004}
8296 }
8297 
8298 @misc{BieliavskyMassar:2001,
8299         abstract = {We present explicit universal strict deformation quantization formulae for actions of Iwasawa subgroups AN of SU(1,n). This answers a question raised by Rieffel.},
8300         author = {P. Bieliavsky and M. Massar},
8301         keywords = {Differential Geometry (math.DG); kw:UDF; Mathematical Physics (math-ph); Quantum Algebra (math.QA); Symplectic Geometry (math.SG)},
8302         localfile = {2001 - Bieliavsky, Massar - Strict Deformation Quantization for Actions of a Class of Symplectic Lie Groups.pdf},
8303         month = jan,
8304         pdf = {http://arxiv.org/pdf/math/0011144},
8305         title = {{Strict Deformation Quantization for Actions of a Class of Symplectic Lie Groups}},
8306         url = {http://arxiv.org/abs/math/0011144},
8307         v1descr = {Mon, 20 Nov 2000 20:36:43 GMT (17kb)},
8308         v1url = {http://www.arxiv.org/abs/math/0011144v1},
8309         v2descr = {Thu, 23 Nov 2000 20:23:42 GMT (17kb)},
8310         v2url = {http://www.arxiv.org/abs/math/0011144v2},
8311         v3descr = {Mon, 15 Jan 2001 19:11:46 GMT (17kb)},
8312         year = {2001}
8313 }
8314 
8315 @book{Nachbin:1964,
8316         author = {L. Nachbin},
8317         localfile = {http://integral.djvu},
8318         title = {{The Haar Integral}},
8319         year = {1964}
8320 }
8321 
8322 @article{LongoWitten:2010,
8323         abstract = {We build up local, time translation covariant Boundary Quantum Field Theory nets of von Neumann algebras A\_V on the Minkowski half-plane \M\_+ starting with a local conformal net A of von Neumann algebras on the real line and an element V of a unitary semigroup E(A) associated with A. The case V=1 reduces to the net\ A\_+ considered by Rehren and one of the authors; if the vacuum character of A is summabl\e A\_V is locally isomorphic \to A\_+. We discuss the structure of the semigroup E(A). By using a one-particle version of Borchers theorem and standard subspace analysis, we provide an abstract analog of the Beurling-Lax theorem that allows us to describe, in particular, all unitaries on the one-particle Hilbert space whose second quantization promotion belongs to of E(A^(0)) with A^(0) the U(1)-current net. Each such unitary is attached to a scattering function or, more generally, to a symmetric inner function. We then obtain families of models via any Buchholz-Mach-Todorov extension of A^(0). A further family of models comes from the Ising model.},
8324         author = {R. Longo and E. Witten},
8325         journal = {Preprint},
8326         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Operator Algebras (math.OA)},
8327         localfile = {2010 - Longo, Witten - An Algebraic Construction of Boundary Quantum Field Theory.pdf},
8328         month = apr,
8329         pdf = {http://arxiv.org/pdf/1004.0616},
8330         title = {{An Algebraic Construction of Boundary Quantum Field Theory }},
8331         url = {http://arxiv.org/abs/1004.0616},
8332         v1descr = {Mon, 5 Apr 2010 11:49:22 GMT (21kb)},
8333         year = {2010}
8334 }
8335 
8336 @article{Araki:1971,
8337         author = {H. Araki},
8338         doi = {10.2977/prims},
8339         eprint = {projecteuclid},
8340         journal = {Publ. Res. Inst. Math. Sci. Kyoto},
8341         localfile = {1970 - Araki - On Quasifree States of CAR and Bogoliubov Automorphisms.pdf},
8342         pages = {385--442},
8343         slaccitation = {\%\%CITATION = PBMAA,6,385\\;\%\%},
8344         title = {{On quasifree states of CAR and Bogoliubov automorphisms}},
8345         url = {http://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=6&iss=3&rank=1&srch=searchterm%7COn+quasifree+states+of+CAR+and+Bogoliubov+automorphisms},
8346         volume = {6},
8347         year = {1971}
8348 }
8349 
8350 @article{Araki:1968,
8351         author = {H. Araki},
8352         journal = {Publ. Res. Inst. Math. Sci. Kyoto University, Ser. A},
8353         localfile = {1968 - Araki - On the Diagonalization of a Bilinear Hamiltonian by a Bogoliubov Transformation.pdf},
8354         pages = {387--412},
8355         title = {{On the diagonalization of a bilinear Hamiltonian by a Bogoliubov transformation}},
8356         volume = {4},
8357         year = {1968}
8358 }
8359 
8360 @article{DappiaggiHackPinamonti:2009,
8361         abstract = {We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We shall explicitly calculate its trace anomaly in particular.},
8362         author = {C. Dappiaggi and {{{{{{{{{{{{{{{{{{{{{{{{{T.-P.}}}}}}}}}}}}}}}}}}}}}}}}} Hack and N. Pinamonti},
8363         doi = {10.1142/S0129055X09003864},
8364         journal = {Rev. Math. Phys.},
8365         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
8366         localfile = {2009 - Dappiaggi, Hack, Pinamonti - The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor.pdf},
8367         pages = {1241--1312},
8368         pdf = {http://arxiv.org/pdf/0904.0612},
8369         title = {{The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor}},
8370         url = {http://arxiv.org/abs/0904.0612},
8371         v1descr = {Fri, 3 Apr 2009 16:08:54 GMT (64kb)},
8372         volume = {21},
8373         year = {2009}
8374 }
8375 
8376 @article{Dimock:1982,
8377         author = {J. Dimock},
8378         coden = {TAMTAM},
8379         doi = {10.2307/1998597},
8380         fjournal = {Transactions of the American Mathematical Society},
8381         issn = {0002-9947},
8382         journal = {Trans. Amer. Math. Soc.},
8383         localfile = {1982 - Dimock - Dirac Quantum Fields on a Manifold.pdf},
8384         mrclass = {81E20 (46L60 81E05)},
8385         mrnumber = {MR637032 (83b:81109)},
8386         mrreviewer = {Ivan F. Wilde},
8387         number = {1},
8388         pages = {133--147},
8389         title = {{Dirac quantum fields on a manifold}},
8390         volume = {269},
8391         year = {1982}
8392 }
8393 
8394 @article{Strohmaier:2000-1,
8395         archiveprefix = {arXiv},
8396         author = {A. Strohmaier},
8397         doi = {10.1007/s002200000299},
8398         eprint = {math-ph/0002054},
8399         journal = {Commun. Math. Phys.},
8400         localfile = {2000 - Strohmaier - The Reeh--Schlieder Property for Quantum Fields on Stationary Spacetimes.pdf},
8401         pages = {105--118},
8402         slaccitation = {\%\%CITATION = MATH-PH/0002054\\;\%\%},
8403         title = {{The Reeh-Schlieder property for quantum fields on stationary spacetimes}},
8404         volume = {215},
8405         year = {2000}
8406 }
8407 
8408 @article{ArakiWyss:1964,
8409         author = {H. Araki and W. Wyss},
8410         journal = {Helv. Phys. Acta},
8411         pages = {136},
8412         title = {{Representations of canonical anticommutation relations}},
8413         volume = {37},
8414         year = {1964}
8415 }
8416 
8417 @article{DoplicherHaagRoberts:1969,
8418         author = {S. Doplicher and R. Haag and J. E. Roberts},
8419         journal = {Commun. Math. Phys.},
8420         localfile = {1969 - Doplicher, Haag, Roberts - Fields, observables and gauge transformations I.pdf},
8421         pages = {1--23},
8422         slaccitation = {\%\%CITATION = CMPHA,13,1\\;\%\%},
8423         title = {{Fields, observables and gauge transformations. I}},
8424         url = {http://projecteuclid.org/euclid.cmp/1103841481},
8425         volume = {13},
8426         year = {1969}
8427 }
8428 
8429 @article{Foit:1983,
8430         author = {J. J. Foit},
8431         journal = {Publ. Res. Inst. Math. Sci. Kyoto},
8432         localfile = {1983 - Foit - Abstract Twisted Duality for Quantum Free Fermi Fields.pdf},
8433         pages = {729--741},
8434         slaccitation = {\%\%CITATION = PBMAA,19,729\\;\%\%},
8435         title = {{Abstract Twisted Duality for Quantum Free Fermi Fields}},
8436         url = {http://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=19&iss=2&rank=11&srch=searchterm%7CAbstract+Twisted+Duality+for+Quantum+Free+Fermi+Fields},
8437         volume = {19},
8438         year = {1983}
8439 }
8440 
8441 @article{Summers:1982,
8442         author = {S. J. Summers},
8443         doi = {10.1007/BF01205664},
8444         journal = {Commun. Math. Phys.},
8445         localfile = {1981 - Summers - Normal product states for fermions and twisted duality for CCR- and CAR-type algebras with application to the Yukawa2 quantum field model.pdf},
8446         pages = {111--141},
8447         slaccitation = {\%\%CITATION = CMPHA,86,111\\;\%\%},
8448         title = {{Normal product states for fermions and twisted duality for CCR- and CAR-type algebras with application to the Yukawa2 quantum field model}},
8449         volume = {86},
8450         year = {1982}
8451 }
8452 
8453 @article{Verch:2001,
8454         archiveprefix = {arXiv},
8455         author = {R. Verch},
8456         doi = {10.1007/s002200100526},
8457         eprint = {math-ph/0102035},
8458         journal = {Commun. Math. Phys.},
8459         localfile = {2001 - Verch - A Spin-Statistics Theorem for Quantum Fields on Curved Spacetime Manifolds in a Generally Covariant Framework.pdf},
8460         pages = {261--288},
8461         slaccitation = {\%\%CITATION = MATH-PH/0102035\\;\%\%},
8462         title = {{A spin-statistics theorem for quantum fields on curved spacetime manifolds in a generally covariant framework}},
8463         volume = {223},
8464         year = {2001}
8465 }
8466 
8467 @article{Verch:2001-1,
8468         archiveprefix = {arXiv},
8469         author = {R. Verch},
8470         eprint = {math-ph/0011026},
8471         journal = {Fields Inst. Commun.},
8472         localfile = {2000 - Verch - On Generalizations of the Spectrum Condition.pdf},
8473         pages = {409--428},
8474         slaccitation = {\%\%CITATION = MATH-PH/0011026\\;\%\%},
8475         title = {{On generalizations of the spectrum condition}},
8476         volume = {30},
8477         year = {2001}
8478 }
8479 
8480 @article{Schweitzer:1993,
8481         author = {L. B. Schweitzer},
8482         doi = {10.1142/S0129167X93000315},
8483         fjournal = {International Journal of Mathematics},
8484         issn = {0129-167X},
8485         journal = {Internat. J. Math.},
8486         localfile = {1993 - Schweitzer - Dense m-convex Frechet Subalgebras of Operator Algebra Crossed Products by Lie Groups.pdf},
8487         mrclass = {46K99 (46A11 46E25 46L05 46L55)},
8488         mrnumber = {MR1232986 (94g:46058)},
8489         mrreviewer = {Keith Taylor},
8490         number = {4},
8491         pages = {601--673},
8492         title = {{Dense {$m$}-convex {F}r\'{e}chet subalgebras of operator algebra crossed products by {L}ie groups}},
8493         url = {http://dx.doi.org/10.1142/S0129167X93000315},
8494         volume = {4},
8495         year = {1993}
8496 }
8497 
8498 @book{Taylor:1986,
8499         author = {M. E. Taylor},
8500         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Taylor - Noncommutative Harmonic Analysis.pdf},
8501         publisher = {American Mathematical Society},
8502         title = {{Noncommutative Harmonic Analysis}},
8503         year = {1986}
8504 }
8505 
8506 @misc{Keyl:2002,
8507         abstract = {In this paper we give a self contained introduction to the conceptional and mathematical foundations of quantum information theory. In the first part we introduce the basic notions like entanglement, channels, teleportation etc. and their mathematical description. The second part is focused on a presentation of the quantitative aspects of the theory. Topics discussed in this context include: entanglement measures, channel capacities, relations between both, additivity and continuity properties and asymptotic rates of quantum operations. Finally we give an overview on some recent developments and open questions.},
8508         author = {M. Keyl},
8509         keywords = {Quantum Physics (quant-ph)},
8510         localfile = {2008 - Keyl - Fundamentals of Quantum Information Theory.pdf},
8511         month = feb,
8512         pdf = {http://arxiv.org/pdf/quant-ph/0202122},
8513         title = {{Fundamentals of Quantum Information Theory}},
8514         url = {http://arxiv.org/abs/quant-ph/0202122},
8515         v1descr = {Thu, 21 Feb 2002 16:52:04 GMT (154kb)},
8516         year = {2002}
8517 }
8518 
8519 @article{PaschkeVerch:2004,
8520         abstract = {A framework which combines ideas from Connes' noncommutative geometry, or spectral geometry, with recent ideas on generally covariant quantum field theory, is proposed in the present work. A certain type of spectral geometries modelling (possibly noncommutative) globally hyperbolic spacetimes is introduced in terms of so-called globally hyperbolic spectral triples. The concept is further generalized to a category of globally hyperbolic spectral geometries whose morphisms describe the generalization of isometric embeddings. Then a local generally covariant quantum field theory is introduced as a covariant functor between such a category of globally hyperbolic spectral geometries and the category of involutive algebras (or *-algebras). Thus, a local covariant quantum field theory over spectral geometries assigns quantum fields not just to a single noncommutative geometry (or noncommutative spacetime), but simultaneously to ``all'' spectral geometries, while respecting the covariance principle demanding that quantum field theories over isomorphic spectral geometries should also be isomorphic. It is suggested that in a quantum theory of gravity a particular class of globally hyperbolic spectral geometries is selected through a dynamical coupling of geometry and matter compatible with the covariance principle.},
8521         author = {M. Paschke and R. Verch},
8522         journal = {Class.Quant.Grav.},
8523         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
8524         localfile = {2004 - Paschke, Verch - Local covariant quantum field theory over spectral geometries.pdf},
8525         pages = {5299--5316},
8526         pdf = {http://arxiv.org/pdf/gr-qc/0405057},
8527         title = {{Local covariant quantum field theory over spectral geometries}},
8528         url = {http://arxiv.org/abs/gr-qc/0405057},
8529         v1descr = {Tue, 11 May 2004 17:05:57 GMT (28kb)},
8530         volume = {21},
8531         year = {2004}
8532 }
8533 
8534 @article{Zahn:2010,
8535         abstract = {Quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential is discussed in two ways: In terms of a continuous set of generalised eigenfunctions of the wave operator, and directly in position space. In both settings, we find a new type of divergence in planar graphs. It is present at and above the self-dual point. This new kind of divergence might make the construction of a Minkowski space version of the Grosse-Wulkenhaar model impossible.},
8536         author = {Jochen Zahn},
8537         journal = {Annales Henri Poincare},
8538         keywords = {High Energy Physics - Theory (hep-th); kw:NC-Wick},
8539         localfile = {2010 - Zahn - Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential.pdf},
8540         pages = {777--804},
8541         pdf = {http://arxiv.org/pdf/1005.0541},
8542         title = {{Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential}},
8543         url = {http://arxiv.org/abs/1005.0541},
8544         v1descr = {Tue, 4 May 2010 14:32:11 GMT (25kb)},
8545         v1url = {http://www.arxiv.org/abs/1005.0541v1},
8546         v2descr = {Tue, 3 May 2011 13:51:19 GMT (26kb)},
8547         volume = {12},
8548         year = {2011}
8549 }
8550 
8551 @misc{AastrupGrimstrupPaschkeNest:2009,
8552         abstract = {We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classical limit of the spectral triple gives the Dirac Hamiltonian in 3+1 dimensions. Also, time-independent lapse and shift fields emerge from the semi-classical states. Our analysis shows that the model might contain fermionic matter degrees of freedom. The semi-classical analysis presented in this paper does away with most of the ambiguities found in the initial semi-finite spectral triple construction. The cubic lattices play the role of a coordinate system and a divergent sequence of free parameters found in the Dirac type operator is identified as a certain inverse infinitesimal volume element.},
8553         author = {J. Aastrup and J. M. Grimstrup and M. Paschke and R. Nest},
8554         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
8555         localfile = {2009 - Aastrup, Grimstrup, Paschke, Nest - On Semi-Classical States of Quantum Gravity and Noncommutative Geometry.pdf},
8556         month = jul,
8557         pdf = {http://arxiv.org/pdf/0907.5510},
8558         title = {{On Semi-Classical States of Quantum Gravity and Noncommutative Geometry}},
8559         url = {http://arxiv.org/abs/0907.5510},
8560         v1descr = {Fri, 31 Jul 2009 11:25:13 GMT (34kb,D)},
8561         year = {2009}
8562 }
8563 
8564 @article{AastrupGrimstrupNest:2008,
8565         abstract = {This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator. The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity. Moreover, the associated Hilbert space corresponds, up to a discrete symmetry group, to the Hilbert space of diffeomorphism invariant states known from Loop Quantum Gravity. Correspondingly, the square of the Dirac operator has, in terms of canonical quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action resembles a partition function of Quantum Gravity. The construction is background independent and is based on an inductive system of triangulations. This paper is the first of two papers on the subject.},
8566         author = {J. Aastrup and J. M. Grimstrup and R. Nest},
8567         doi = {10.1088/0264-9381},
8568         journal = {Class. Quant. Grav.},
8569         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
8570         localfile = {2008 - Aastrup, Grimstrup, Nest - On Spectral Triples in Quantum Gravity.pdf},
8571         month = feb,
8572         number = {26},
8573         pages = {065011},
8574         pdf = {http://arxiv.org/pdf/0802.1783},
8575         title = {{On Spectral Triples in Quantum Gravity I}},
8576         url = {http://arxiv.org/abs/0802.1783},
8577         v1descr = {Wed, 13 Feb 2008 11:12:49 GMT (76kb)},
8578         year = {2008}
8579 }
8580 
8581 @article{BlaschkeGieresKronbergerSchwedaWohlgenannt:2008,
8582         abstract = {Motivated by the recent construction of a translation-invariant renormalizable non-commutative model for a scalar field (see arXiv:0802.0791 [math-ph]), we introduce models for non-commutative U(1) gauge fields along the same lines. More precisely, we include some extra terms into the action with the aim of getting rid of the UV/IR mixing.},
8583         author = {D. Blaschke and F. Gieres and E. Kronberger and M. Schweda and M. Wohlgenannt},
8584         doi = {10.1088/1751-8113},
8585         journal = {J.Phys.A},
8586         keywords = {High Energy Physics - Theory (hep-th)},
8587         localfile = {2008 - Blaschke, Gieres, Kronberger, Schweda, Wohlgenannt - Translation-invariant models for non-commutative gauge fields.pdf},
8588         pages = {252002},
8589         pdf = {http://arxiv.org/pdf/0804.1914},
8590         title = {{Translation-invariant models for non-commutative gauge fields}},
8591         url = {http://arxiv.org/abs/0804.1914},
8592         v1descr = {Fri, 11 Apr 2008 15:25:50 GMT (8kb)},
8593         volume = {41},
8594         year = {2008}
8595 }
8596 
8597 @article{AschieriBlohmannDimitrijevicMeyerSchuppWess:2005,
8598         abstract = {A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter theta. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different from the undeformed one. Based on this deformed algebra a covariant tensor calculus is constructed and all the concepts like metric, covariant derivatives, curvature and torsion can be defined on the deformed space as well. The construction of these geometric quantities is presented in detail. This leads to an action invariant under the deformed diffeomorphism algebra and can be interpreted as a theta-deformed Einstein-Hilbert action. The metric or the vierbein field will be the dynamical variable as they are in the undeformed theory. The action and all relevant quantities are expanded up to second order in theta.},
8599         author = {P. Aschieri and C. Blohmann and M. Dimitrijevic and F. Meyer and P. Schupp and J. Wess},
8600         doi = {10.1088/0264-9381},
8601         journal = {Class.Quant.Grav.},
8602         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
8603         localfile = {2005 - Aschieri, Blohmann, Dimitrijevic, Meyer, Schupp, Wess - A Gravity Theory on Noncommutative Spaces.pdf},
8604         pages = {3511--3532},
8605         pdf = {http://arxiv.org/pdf/hep-th/0504183},
8606         title = {{A Gravity Theory on Noncommutative Spaces}},
8607         url = {http://arxiv.org/abs/hep-th/0504183},
8608         v1descr = {Fri, 22 Apr 2005 13:05:16 GMT (38kb)},
8609         v1url = {http://www.arxiv.org/abs/hep-th/0504183v1},
8610         v2descr = {Thu, 12 May 2005 17:52:30 GMT (38kb)},
8611         v2url = {http://www.arxiv.org/abs/hep-th/0504183v2},
8612         v3descr = {Tue, 16 Aug 2005 14:38:18 GMT (38kb)},
8613         volume = {22},
8614         year = {2005}
8615 }
8616 
8617 @article{OsterwalderSchrader:1975,
8618         author = {K. Osterwalder and R. Schrader},
8619         doi = {10.1007/BF01608978},
8620         journal = {Commun. Math. Phys.},
8621         keywords = {kw:NC-Wick},
8622         localfile = {1975 - Osterwalder, Schrader - Axioms for Euclidean Green's functions II.pdf},
8623         pages = {281},
8624         slaccitation = {\%\%CITATION = CMPHA,42,281\\;\%\%},
8625         title = {{Axioms for Euclidean Green's Functions. 2}},
8626         url = {http://projecteuclid.org/euclid.cmp/1103899050},
8627         volume = {42},
8628         x-color = {#19ffd1},
8629         year = {1975}
8630 }
8631 
8632 @article{Zinoviev:1995,
8633         abstract = {The new inversion formula for the Laplace transformation of the tempered distributions with supports in the closed positive semiaxis is obtained. The inverse Laplace transform of the tempered distribution is defined by means of the limit of the special distribution constructed from this distribution. The weak spectral condition on the Euclidean Green's functions requires that some of the limits needed for the inversion formula exist for any Euclidean Green's function with even number of variables. We prove that the initial Osterwalder--Schrader axioms (1973) and the weak spectral condition are equivalent with the Wightman axioms.},
8634         author = {Yu.M. Zinoviev},
8635         journal = {Commun. Math. Phys.},
8636         keywords = {High Energy Physics - Theory (hep-th)},
8637         localfile = {1995 - Zinoviev - Equivalence of Euclidean and Wightman field theories.pdf},
8638         pages = {1--28},
8639         pdf = {http://arxiv.org/pdf/hep-th/9408009},
8640         title = {{Equivalence of the Euclidean and Wightman Field Theories}},
8641         url = {http://arxiv.org/abs/hep-th/9408009},
8642         v1descr = {Tue, 2 Aug 1994 11:15:50 GMT (20kb)},
8643         volume = {174},
8644         year = {1995}
8645 }
8646 
8647 @article{BahnsDoplicherFredenhagenPiacitelli:2010,
8648         abstract = {We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra. In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes. The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity. The Euclidean distance operator is shown to have spectrum bounded below by a constant of the order of the Planck length. The corresponding statement is proved also for both the space-space and space-time area operators, as well as for the Euclidean length of the vector representing the 3-volume operators. However, the space 3-volume operator (the time component of that vector) is shown to have spectrum equal to the whole complex plane. All these operators are normal, while the distance operators are also selfadjoint. The Lorentz invariant spacetime volume operator, representing the 4- volume spanned by five independent events, is shown to be normal. Its spectrum is pure point with a finite distance (of the order of the fourth power of the Planck length) away from the origin. The mathematical formalism apt to these problems is developed and its relation to a general formulation of Gauge Theories on Quantum Spaces is outlined. As a byproduct, a Hodge Duality between the absolute dif- ferential and the Hochschild boundary is pointed out.},
8649         author = {D. Bahns and S. Doplicher and K. Fredenhagen and G. Piacitelli},
8650         journal = {Preprint},
8651         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
8652         localfile = {2010 - Bahns, Doplicher, Fredenhagen, Piacitelli - Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators.pdf},
8653         month = may,
8654         pdf = {http://arxiv.org/pdf/1005.2130},
8655         title = {{Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators }},
8656         url = {http://arxiv.org/abs/1005.2130},
8657         v1descr = {Wed, 12 May 2010 15:34:41 GMT (25kb)},
8658         year = {2010}
8659 }
8660 
8661 @article{SummersWerner:1987,
8662         author = {S. J. Summers and R. Werner},
8663         doi = {10.1063/1.527733},
8664         journal = {J. Math. Phys.},
8665         localfile = {1987 - Summers, Werner - Bell's Inequalities and quantum field theory I. General setting.pdf},
8666         pages = {2440--2447},
8667         slaccitation = {\%\%CITATION = JMAPA,28,2440\\;\%\%},
8668         title = {{Bells Inequalities and quantum field theory I. General setting}},
8669         volume = {28},
8670         x-color = {#ff9bfa},
8671         year = {1987}
8672 }
8673 
8674 @misc{Rieffel:1997,
8675         abstract = {The purpose of this note is to show that the construction of the C*-algebra for the space-time uncertainty relations which was introduced by Doplicher, Fredenhagen and Roberts fits comfortably into the strict deformation quantization construction introduced earlier by the author.},
8676         author = {M. A. Rieffel},
8677         keywords = {Functional Analysis (math.FA); Operator Algebras (math.OA)},
8678         localfile = {1997 - Rieffel - On the operator algebra for the space-time uncertainty relations.pdf},
8679         month = jan,
8680         pdf = {http://arxiv.org/pdf/funct-an/9701011},
8681         title = {{On the operator algebra for the space-time uncertainty relations}},
8682         url = {http://arxiv.org/abs/funct-an/9701011},
8683         v1descr = {Wed, 29 Jan 1997 00:24:41 GMT (10kb)},
8684         year = {1997}
8685 }
8686 
8687 @book{Lang:1975,
8688         author = {S. Lang},
8689         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Lang - SL(2,R).djvu},
8690         publisher = {Springer},
8691         title = {{SL\_2(R)}},
8692         year = {1975}
8693 }
8694 
8695 @article{BuchholzDAntoniLongo:2007,
8696         abstract = {We introduce a new type of spectral density condition, that we call L^2-nuclearity. One formulation concerns lowest weight unitary representations of SL(2,R) and turns out to be equivalent to the existence of characters. A second formulation concerns inclusions of local observable von Neumann algebras in Quantum Field Theory. We show the two formulations to agree in chiral Conformal QFT and, starting from the trace class condition for the semigroup generated by the conformal Hamiltonian L\_0, we infer and naturally estimate the Buchholz-Wichmann nuclearity condition and the (distal) split property. As a corollary, if \L\_0 is log-elliptic, the Buchholz-Junglas set up is realized and so there exists a beta-KMS state for the translation dynamics on the net of C*-algebras for every inverse temperature beta>0. We include further discussions on higher dimensional spacetimes. In particular, we verify that L^2-nuclearity is satisfied for the scalar, massless Klein-Gordon field.},
8697         author = {D. Buchholz and C. D'Antoni and R. Longo},
8698         journal = {Commun. Math. Phys.},
8699         keywords = {Mathematical Physics (math-ph); Operator Algebras (math.OA); kw:scaling},
8700         localfile = {2006 - Buchholz, D'Antoni, Longo - Nuclearity and Thermal States in Conformal Field Theory.pdf},
8701         pages = {267--293},
8702         pdf = {http://arxiv.org/pdf/math-ph/0603083},
8703         title = {{Nuclearity and Thermal States in Conformal Field Theory}},
8704         url = {http://arxiv.org/abs/math-ph/0603083},
8705         v1descr = {Thu, 30 Mar 2006 13:30:28 GMT (25kb)},
8706         v1url = {http://www.arxiv.org/abs/math-ph/0603083v1},
8707         v2descr = {Thu, 16 Nov 2006 16:33:11 GMT (26kb)},
8708         volume = {270},
8709         year = {2007}
8710 }
8711 
8712 @book{Dixmier:1977,
8713         address = {Amsterdam, New York, Oxford},
8714         author = {J. Dixmier},
8715         localfile = {http://c-algebras.djvu},
8716         publisher = {North-Holland-Publishing Company},
8717         title = {{C*-Algebras}},
8718         year = {1977}
8719 }
8720 
8721 @article{Jaekel:2000,
8722         abstract = {We show that the Reeh-Schlieder property w.r.t. the KMS-vector is a direct consequence of locality, additivity and the relativistic KMS-condition. The latter characterises the thermal equilibrium states of a relativistic quantum field theory. The statement remains vaild even if the given equilibrium state breaks spatial translation invariance.},
8723         author = {C. D. J{\"{a}}kel},
8724         journal = {J.Math.Phys.},
8725         keywords = {High Energy Physics - Theory (hep-th)},
8726         localfile = {1999 - J\"{a}kel - The Reeh-Schlieder property for thermal field theories.pdf},
8727         pages = {1745--1754},
8728         pdf = {http://arxiv.org/pdf/hep-th/9904049},
8729         title = {{The Reeh-Schlieder property for thermal field theories}},
8730         url = {http://arxiv.org/abs/hep-th/9904049},
8731         v1descr = {Wed, 7 Apr 1999 09:47:22 GMT (13kb)},
8732         v1url = {http://www.arxiv.org/abs/hep-th/9904049v1},
8733         v2descr = {Wed, 5 May 2004 08:59:15 GMT (13kb)},
8734         volume = {41},
8735         year = {2000}
8736 }
8737 
8738 @article{Sanders:2009-2,
8739         abstract = {We describe the free Dirac field in a four dimensional spacetime as a locally covariant quantum field theory in the sense of Brunetti, Fredenhagen and Verch, using a representation independent construction. The freedom in the geometric constructions involved can be encoded in terms of the cohomology of the category of spin spacetimes. If we restrict ourselves to the observable algebra the cohomological obstructions vanish and the theory is unique. We establish some basic properties of the theory and discuss the class of Hadamard states, filling some technical gaps in the literature. Finally we show that the relative Cauchy evolution yields commutators with the stress-energy-momentum tensor, as in the scalar field case.},
8740         author = {K. Sanders},
8741         doi = {10.1142/S0129055X10003990},
8742         journal = {Rev. Math. Phys.},
8743         keywords = {Mathematical Physics (math-ph)},
8744         localfile = {2010 - Sanders - The locally covariant Dirac field.pdf},
8745         number = {4},
8746         pages = {381--430},
8747         pdf = {http://arxiv.org/pdf/0911.1304},
8748         title = {{The locally covariant Dirac field}},
8749         url = {http://arxiv.org/abs/0911.1304},
8750         v1descr = {Fri, 6 Nov 2009 17:17:11 GMT (48kb)},
8751         v1url = {http://www.arxiv.org/abs/0911.1304v1},
8752         v2descr = {Wed, 11 Nov 2009 14:40:24 GMT (48kb)},
8753         volume = {22},
8754         year = {2010}
8755 }
8756 
8757 @article{MukhanovFeldmanBrandenberger:1990,
8758         author = {V. F. Mukhanov and H. A. Feldman and R. H. Brandenberger},
8759         doi = {10.1016/0370-1573(92)90044-Z},
8760         journal = {Phys. Rept.},
8761         pages = {203--333},
8762         slaccitation = {\%\%CITATION = PRPLC,215,203\\;\%\%},
8763         title = {{Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions}},
8764         volume = {215},
8765         year = {1992}
8766 }
8767 
8768 @article{EstradaGracia-BondiaVarilly:1989,
8769         author = {R. Estrada and J. M. Gracia-Bondia and J. C. Varilly},
8770         doi = {10.1063/1.528514},
8771         journal = {J. Math. Phys.},
8772         localfile = {1989 - Estrada, Gracia-Bondia, Varilly - On asymptotic expansions of twisted products.pdf},
8773         pages = {2789--2796},
8774         slaccitation = {\%\%CITATION = JMAPA,30,2789\\;\%\%},
8775         title = {{On Asymptotic expansions of twisted products}},
8776         volume = {30},
8777         year = {1989}
8778 }
8779 
8780 @book{Jackson:1962,
8781         author = {J. D. Jackson},
8782         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Jackson J.D. Classical electrodynamics (Wiley, 1962)(T)(656s).djvu},
8783         title = {{Classical Electrodynamics}},
8784         year = {1962}
8785 }
8786 
8787 @misc{Kasprzak:2010,
8788         abstract = {Let G be a locally compact group, H an abelian subgroup and let f be a continuous 2-cocycle on the dual group of H. Let B be a C*-algebra equipped with a continuous right coaction of G. Using Rieffel deformation, we can construct a quantum group G(f) and the deformed C*-algebra B(f). The aim of this paper is to show that B(f) is equipped with a continuous coaction of G(f). The transition from the original coaction to its deformed counterpart is nontrivial in the sense that the deformed one contains complete information about the undeformed one. In order to illustrate our construction we apply it to the action of the Lorentz group on the Minkowski space obtaining a C*-algebraic quantum Minkowski space.},
8789         author = {P. Kasprzak},
8790         keywords = {Operator Algebras (math.OA)},
8791         localfile = {2010 - Kasprzak - Rieffel deformation of group coactions.pdf},
8792         month = jun,
8793         pdf = {http://arxiv.org/pdf/1006.3416},
8794         title = {{Rieffel deformation of group coactions}},
8795         url = {http://arxiv.org/abs/1006.3416},
8796         v1descr = {Thu, 17 Jun 2010 10:12:06 GMT (18kb)},
8797         year = {2010}
8798 }
8799 
8800 @book{Borchers:1996-1,
8801         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
8802         localfile = {http://theory.djvu},
8803         publisher = {Springer},
8804         title = {{Translation Group and Particle Representations in Quantum Field Theory}},
8805         year = {1996}
8806 }
8807 
8808 @article{ChuMadoreSteinacker:2001,
8809         abstract = {We study the one loop dynamics of QFT on the fuzzy sphere and calculate the planar and nonplanar contributions to the two point function at one loop. We show that there is no UV/IR mixing on the fuzzy sphere. The fuzzy sphere is characterized by two moduli: a dimensionless parameter N and a dimensionful radius R. Different geometrical phases can obtained at different corners of the moduli space. In the limit of the commutative sphere, we find that the two point function is regular without UV/IR mixing; however quantization does not commute with the commutative limit, and a finite ``noncommutative anomaly'' survives in the commutative limit. In a different limit, the noncommutative plane R^2\_theta is obtained, and the UV/IR mixing reappears. This provides an explanation of the UV/IR mixing as an infinite variant of the ``noncommutative anomaly''.},
8810         author = {{{{{{{{{{{{{{{{{{{{{{{{{{C.-S.}}}}}}}}}}}}}}}}}}}}}}}}} Chu and J. Madore and H. Steinacker},
8811         journal = {JHEP},
8812         keywords = {High Energy Physics - Theory (hep-th)},
8813         localfile = {2001 - Chu, Madore, Steinacker - Scaling Limits of the Fuzzy Sphere at one Loop.pdf},
8814         pages = {038},
8815         pdf = {http://arxiv.org/pdf/hep-th/0106205},
8816         title = {{Scaling Limits of the Fuzzy Sphere at one Loop}},
8817         url = {http://arxiv.org/abs/hep-th/0106205},
8818         v1descr = {Fri, 22 Jun 2001 11:38:21 GMT (16kb)},
8819         v1url = {http://www.arxiv.org/abs/hep-th/0106205v1},
8820         v2descr = {Tue, 21 Aug 2001 20:31:29 GMT (17kb)},
8821         volume = {0108},
8822         year = {2001}
8823 }
8824 
8825 @article{Rieffel:2002,
8826         abstract = {On looking at the literature associated with string theory one finds statements that a sequence of matrix algebras converges to the 2-sphere (or to other spaces). There is often careful bookkeeping with lengths, which suggests that one is dealing with ``quantum metric spaces''. We show how to make these ideas precise by means of Berezin quantization using coherent states. We work in the general setting of integral coadjoint orbits for compact Lie groups.},
8827         author = {M. A. Rieffel},
8828         keywords = {High Energy Physics - Theory (hep-th); Metric Geometry (math.MG); Operator Algebras (math.OA); Quantum Physics (quant-ph); Representation Theory (math.RT)},
8829         localfile = {2001 - Rieffel - Matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance.pdf},
8830         month = dec,
8831         pdf = {http://arxiv.org/pdf/math/0108005},
8832         title = {{Matrix algebras converge to the sphere for quantum Gromov--Hausdorff distance}},
8833         url = {http://arxiv.org/abs/math/0108005},
8834         v1descr = {Wed, 1 Aug 2001 19:08:16 GMT (25kb)},
8835         v1url = {http://www.arxiv.org/abs/math/0108005v1},
8836         v2descr = {Thu, 12 Dec 2002 19:58:42 GMT (26kb)},
8837         year = {2002}
8838 }
8839 
8840 @article{DybalskiTanimoto:2010,
8841         abstract = {This paper presents the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete. These two-dimensional models are obtained by an application of a deformation procedure, introduced recently by Grosse and Lechner, to chiral conformal quantum field theories. The resulting models may not be strictly local, but they contain observables localized in spacelike wedges.},
8842         author = {W. Dybalski and Y. Tanimoto},
8843         journal = {Preprint},
8844         keywords = {High Energy Physics - Theory (hep-th); kw:warping; Mathematical Physics (math-ph)},
8845         localfile = {2010 - Dybalski, Tanimoto - Asymptotic completeness in a class of massless relativistic quantum field theories.pdf},
8846         month = jun,
8847         pdf = {http://arxiv.org/pdf/1006.5430},
8848         title = {{Asymptotic completeness in a class of massless relativistic quantum field theories }},
8849         url = {http://arxiv.org/abs/1006.5430},
8850         v1descr = {Mon, 28 Jun 2010 18:34:55 GMT (16kb)},
8851         year = {2010}
8852 }
8853 
8854 @article{FrohlichOsterwalderSeiler:1983,
8855         author = {J. Fr{\"{o}}hlich and K. Osterwalder and E. Seiler},
8856         journal = {Annals Math.},
8857         keywords = {kw:NC-Wick},
8858         localfile = {1983 - Fr\"{o}hlich, Osterwalder, Seiler - On Virtual representations of symmetric spaces and their analytic continuation.pdf},
8859         pages = {461--489},
8860         slaccitation = {\%\%CITATION = ANMAA,118,461\\;\%\%},
8861         title = {{On Virtual representations of symmetric spaces and their analytic continuation}},
8862         url = {http://www.jstor.org/stable/2006979},
8863         volume = {118},
8864         x-color = {#19ffd1},
8865         year = {1983}
8866 }
8867 
8868 @book{Helgason:1962,
8869         author = {S. Helgason},
8870         localfile = {http://spaces.djvu},
8871         publisher = {Academic Press},
8872         title = {{Differential Geometry and Symmetric Spaces}},
8873         year = {1962}
8874 }
8875 
8876 @article{Seiler:1982,
8877         author = {E. Seiler},
8878         journal = {Lect. Notes Phys.},
8879         keywords = {kw:NC-Wick},
8880         localfile = {http://mechanics.djvu},
8881         pages = {1--192},
8882         slaccitation = {\%\%CITATION = LNPHA,159,1\\;\%\%},
8883         title = {{Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics}},
8884         volume = {159},
8885         year = {1982}
8886 }
8887 
8888 @misc{AcharyyaVaidya:2010,
8889         abstract = {In Minkowski space, an accelerated reference frame may be defined as one that is related to an inertial frame by a sequence of instantaneous Lorentz transformations. Such an accelerated observer sees a causal horizon, and the quantum vacuum of the inertial observer appears thermal to the accelerated observer, also known as the Unruh effect. We argue that an accelerating frame may be similarly defined (i.e. as a sequence of instantaneous Lorentz transformations) in noncommutative Moyal spacetime, and discuss the twisted quantum field theory appropriate for such an accelerated observer. Our analysis shows that there are several new features in the case of noncommutative spacetime: chiral massless fields in $(1+1)$ dimensions have a qualitatively different behavior compared to massive fields. In addition, the vacuum of the inertial observer is no longer an equilibrium thermal state of the accelerating observer, and the Bose-Einstein distribution acquires $\theta$-dependent corrections.},
8890         author = {N. Acharyya and S. Vaidya},
8891         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
8892         localfile = {2010 - Acharyya, Vaidya - Uniformly Accelerated Observer in Moyal Spacetime.pdf},
8893         month = jun,
8894         pdf = {http://arxiv.org/pdf/1005.4666},
8895         title = {{Uniformly Accelerated Observer in Moyal Spacetime}},
8896         url = {http://arxiv.org/abs/1005.4666},
8897         v1descr = {Tue, 25 May 2010 19:25:19 GMT (21kb)},
8898         v1url = {http://www.arxiv.org/abs/1005.4666v1},
8899         v2descr = {Wed, 2 Jun 2010 15:17:03 GMT (21kb)},
8900         v2url = {http://www.arxiv.org/abs/1005.4666v2},
8901         v3descr = {Mon, 7 Jun 2010 14:18:59 GMT (21kb)},
8902         year = {2010}
8903 }
8904 
8905 @book{Kirillov:2004,
8906         author = {A.A. Kirillov},
8907         keywords = {kw:UDF},
8908         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Kirillov - Lectures on the Orbit Method.pdf},
8909         publisher = {American Mathematical Society},
8910         title = {{Lectures on the Orbit Method}},
8911         year = {2004}
8912 }
8913 
8914 @misc{BieliavskyGurauRivasseau:2008,
8915         abstract = {Quantum field theory has been shown recently renormalizable on flat Moyal space and better behaved than on ordinary space-time. Some models at least should be completely finite, even beyond perturbation theory. In this paper a first step is taken to extend such theories to non-flat backgrounds such as solvable symmetric spaces.},
8916         author = {P. Bieliavsky and R. Gurau and V. Rivasseau},
8917         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Symplectic Geometry (math.SG); kw:UDF},
8918         localfile = {2008 - Bieliavsky, Gurau, Rivasseau - Non Commutative Field Theory on Rank One Symmetric Spaces.pdf},
8919         month = jun,
8920         pdf = {http://arxiv.org/pdf/0806.4255},
8921         title = {{Non Commutative Field Theory on Rank One Symmetric Spaces}},
8922         url = {http://arxiv.org/abs/0806.4255},
8923         v1descr = {Thu, 26 Jun 2008 18:33:06 GMT (26kb)},
8924         year = {2008}
8925 }
8926 
8927 @article{CushmanKallen:2006,
8928         abstract = {In this paper we give an effective method for finding a unique representative of each orbit of the adjoint and coadjoint action of the real affine orthogonal group on its Lie algebra. In both cases there are orbits which have a modulus that is different from the usual invariants for orthogonal groups. We find an unexplained bijection between adjoint and coadjoint orbits. As a special case, we classify the adjoint and coadjoint orbits of the Poincar\'{e} group.},
8929         author = {R. Cushman and W. van der Kallen},
8930         journal = {Acta Appl Math},
8931         keywords = {kw:UDF; Representation Theory (math.RT)},
8932         localfile = {2006 - Cushman, van der Kallen - Adjoint and Coadjoint Orbits of the Poincare Group.pdf},
8933         pages = {65--89},
8934         pdf = {http://arxiv.org/pdf/math/0305442},
8935         title = {{Adjoint and coadjoint orbits of the Poincar\'{e} group}},
8936         ur