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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\>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^- -\> e^- + e^- and \gamma + e^- \-\> \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^-\ -\> 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 -\> \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\>2. When \n\>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\>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\>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}},