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 @article{Doplicher:1965,
         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.},
         author = {S. Doplicher},
         journal = {Commun. Math. Phys.},
         pages = {1--5},
         slaccitation = {\%\%CITATION = CMPHA,16,138\\;\%\%},
         title = {{An algebraic spectrum condition}},
         url = {http://projecteuclid.org/euclid.cmp/1103757611},
         volume = {1},
         year = {1965}
 }
 
 @article{Borchers:1969,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Commun. Math. Phys.},
         localfile = {1969 - Borchers - On the Implementability of Automorphism Groups.pdf},
         pages = {305--314},
         slaccitation = {\%\%CITATION = CMPHA,14,305\\;\%\%},
         title = {{On the implementability of automorphism groups}},
         url = {http://projecteuclid.org/euclid.cmp/1103841819},
         volume = {14},
         year = {1969}
 }
 
 @article{EpsteinGlaserMartin:1969,
         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.},
         author = {H. Epstein and V. Glaser and A. Martin},
         journal = {Commun. Math. Phys.},
         localfile = {1969 - Epstein, Glaser, Martin - Polynomial behaviour of scattering amplitudes at fixed momentum transfer in theories with local observables.pdf},
         pages = {257--316},
         slaccitation = {\%\%CITATION = CMPHA,13,257\\;\%\%},
         title = {{Polynomial behaviour of scattering amplitudes at fixed momentum transfer in theories with local observables}},
         url = {http://projecteuclid.org/euclid.cmp/1103841627},
         volume = {13},
         year = {1969}
 }
 
 @article{GlimmJaffe:1971-1,
         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.},
         author = {J. Glimm and A. Jaffe},
         journal = {Commun. Math. Phys.},
         localfile = {1971 - Glimm, Jaffe - The energy momentum spectrum and vacuum expectation values in quantum field theory II.pdf},
         pages = {1--22},
         slaccitation = {\%\%CITATION = CMPHA,22,1\\;\%\%},
         title = {{The energy momentum spectrum and vacuum expectation values in quantum field theory, ii}},
         url = {http://projecteuclid.org/euclid.cmp/1103857409},
         volume = {22},
         year = {1971}
 }
 
 @article{BorchersHegerfeldt:1972,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and G. C. Hegerfeldt},
         journal = {Commun. Math. Phys.},
         localfile = {1972 - Borchers, Hegerfeldt - The Structure of Space-Time Transformations.pdf},
         pages = {259--266},
         slaccitation = {\%\%CITATION = CMPHA,28,259\\;\%\%},
         title = {{The structure of space-time transformations}},
         url = {http://projecteuclid.org/euclid.cmp/1103858408},
         volume = {28},
         year = {1972}
 }
 
 @article{Woronowicz:1972,
         author = {S. L. Woronowicz},
         journal = {Commun. Math. Phys.},
         localfile = {1972 - Woronowicz - On the Purification of Factor States.pdf},
         pages = {221--235},
         slaccitation = {\%\%CITATION = CMPHA,28,221\\;\%\%},
         title = {{On the purification of factor states}},
         volume = {28},
         year = {1972}
 }
 
 @article{Buchholz:1975-1,
         author = {D. Buchholz},
         journal = {Commun. Math. Phys.},
         localfile = {1974 - Buchholz - Collision theory for massless Fermions.pdf},
         pages = {269},
         slaccitation = {\%\%CITATION = CMPHA,42,269\\;\%\%},
         title = {{Collision Theory for Massless Fermions}},
         volume = {42},
         year = {1975}
 }
 
 @article{Buchholz:1974-1,
         author = {D. Buchholz},
         journal = {Commun. Math. Phys.},
         localfile = {1974 - Buchholz - Haag-Ruelle approximation of collision states.pdf},
         pages = {243--253},
         slaccitation = {\%\%CITATION = CMPHA,36,243\\;\%\%},
         title = {{Haag-ruelle approximation of collision states}},
         volume = {36},
         year = {1974}
 }
 
 @article{Buchholz:1974-2,
         author = {D. Buchholz},
         journal = {Commun. Math. Phys.},
         localfile = {1974 - Buchholz - Product states for local algebras.pdf},
         pages = {287--304},
         slaccitation = {\%\%CITATION = CMPHA,36,287\\;\%\%},
         title = {{Product States for Local Algebras}},
         volume = {36},
         year = {1974}
 }
 
 @article{FannesVerbeure:1974,
         author = {M. Fannes and A. Verbeure},
         journal = {Commun. Math. Phys.},
         localfile = {1974 - Fannes, Verbeure - On the time evolution automorphisms of the CCR-algebra for quantum mechanics.pdf},
         pages = {257--264},
         slaccitation = {\%\%CITATION = CMPHA,35,257\\;\%\%},
         title = {{On the time evolution automorphisms of the ccr-algebra for quantum mechanics}},
         volume = {35},
         year = {1974}
 }
 
 @article{BorchersSen:1975,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and R. N. Sen},
         journal = {Commun. Math. Phys.},
         localfile = {1975 - Borchers, Sen - Relativity groups in the presence of matter.pdf},
         pages = {101},
         slaccitation = {\%\%CITATION = CMPHA,42,101\\;\%\%},
         title = {{Relativity Groups in the Presence of Matter}},
         volume = {42},
         year = {1975}
 }
 
 @article{BorchersYngvason:1975,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and J. Yngvason},
         journal = {Commun. Math. Phys.},
         localfile = {1975 - Borchers, Yngvason - Integral representations for Schwinger functionals and the moment problem over nuclear spaces.pdf},
         pages = {255},
         slaccitation = {\%\%CITATION = CMPHA,43,255\\;\%\%},
         title = {{Integral Representations for Schwinger Functionals and the Moment Problem over Nuclear Spaces}},
         volume = {43},
         year = {1975}
 }
 
 @article{BorchersYngvason:1975-1,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and J. Yngvason},
         journal = {Commun. Math. Phys.},
         localfile = {1975 - Borchers, Yngvason - On the algebra of field operators. The weak commutant and integral decompositions of states.pdf},
         pages = {231},
         slaccitation = {\%\%CITATION = CMPHA,42,231\\;\%\%},
         title = {{On the Algebra of Field Operators: The Weak Commutant and Integral Decompositions of States}},
         volume = {42},
         year = {1975}
 }
 
 @article{Driessler:1975,
         author = {W. Driessler},
         journal = {Commun. Math. Phys.},
         localfile = {1975 - Driessler - Comments on lightlike translations and applications in relativistic quantum field theory.pdf},
         pages = {133--141},
         slaccitation = {\%\%CITATION = CMPHA,44,133\\;\%\%},
         title = {{Comments on Lightlike Translations and Applications in Relativistic Quantum Field Theory}},
         volume = {44},
         year = {1975}
 }
 
 @article{BorchersYngvason:1976,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and J. Yngvason},
         journal = {Commun. Math. Phys.},
         localfile = {1976 - Borchers, Yngvason - Necessary and sufficient conditions for integral representations of Wightman functionals at Schwinger points.pdf},
         pages = {197},
         slaccitation = {\%\%CITATION = CMPHA,47,197\\;\%\%},
         title = {{Necessary and Sufficient Conditions for Integral Representations of Wightman Functionals at Schwinger Points}},
         volume = {47},
         year = {1976}
 }
 
 @article{BuchholzRoberts:1976,
         author = {D. Buchholz and J. E. Roberts},
         journal = {Commun. Math. Phys.},
         localfile = {1976 - Buchholz, Roberts - Bounded perturbations of dynamics.pdf},
         pages = {161},
         slaccitation = {\%\%CITATION = CMPHA,49,161\\;\%\%},
         title = {{Bounded Perturbations of Dynamics}},
         volume = {49},
         year = {1976}
 }
 
 @article{Buchholz:1977,
         author = {D. Buchholz},
         journal = {Commun. Math. Phys.},
         localfile = {1977 - Buchholz - Collision theory for massless bosons.pdf},
         pages = {147},
         slaccitation = {\%\%CITATION = CMPHA,52,147\\;\%\%},
         title = {{Collision Theory for Massless Bosons}},
         volume = {52},
         year = {1977}
 }
 
 @article{BuchholzFredenhagen:1977,
         author = {D. Buchholz and K. Fredenhagen},
         journal = {Commun. Math. Phys.},
         localfile = {1977 - Buchholz, Fredenhagen - A note on the inverse scattering problem in quantum field theory.pdf},
         pages = {91},
         slaccitation = {\%\%CITATION = CMPHA,56,91\\;\%\%},
         title = {{A Note on the Inverse Scattering Problem in Quantum Field Theory}},
         volume = {56},
         year = {1977}
 }
 
 @article{Iagolnitzer:1978,
         author = {D. Iagolnitzer},
         journal = {Phys. Rev.},
         localfile = {1978 - Iagolnitzer - Factorization of the multiparticle S-matrix in two-dimensional space-time models.pdf},
         pages = {1275},
         slaccitation = {\%\%CITATION = PHRVA,D18,1275\\;\%\%},
         title = {{Factorization of the Multiparticle S-Matrix in two-dimensional Space-Time Models}},
         volume = {D18},
         year = {1978}
 }
 
 @article{PuszWoronowicz:1978,
         author = {W. Pusz and S. L. Woronowicz},
         journal = {Commun. Math. Phys.},
         localfile = {1978 - Pusz, Woronowicz - Passive States and KMS States for General Quantum Systems.pdf},
         pages = {273--290},
         slaccitation = {\%\%CITATION = CMPHA,58,273\\;\%\%},
         title = {{Passive States and KMS States for General Quantum Systems}},
         volume = {58},
         year = {1978}
 }
 
 @article{ShankarWitten:1978,
         author = {R. Shankar and E. Witten},
         journal = {Phys. Rev.},
         localfile = {1978 - Shankar, Witten - S-matrix of the supersymmetric nonlinear sigma model.pdf},
         pages = {2134},
         slaccitation = {\%\%CITATION = PHRVA,D17,2134\\;\%\%},
         title = {{THE S MATRIX OF THE SUPERSYMMETRIC NONLINEAR sigma MODEL}},
         volume = {D17},
         year = {1978}
 }
 
 @article{Longo:1979,
         author = {R. Longo},
         journal = {Commun. Math. Phys.},
         localfile = {1979 - Longo - Notes on algebraic invariants for noncommutative dynamical systems.pdf},
         pages = {195--207},
         slaccitation = {\%\%CITATION = CMPHA,69,195\\;\%\%},
         title = {{Notes on algebraic invariants for noncommutative dynamical systems}},
         volume = {69},
         year = {1979}
 }
 
 @article{EpsteinGlaserIagolnitzer:1981,
         author = {H. Epstein and V. Glaser and D. Iagolnitzer},
         journal = {Commun. Math. Phys.},
         localfile = {1981 - Epstein, Glaser, Iagolnitzer - SOME ANALYTICITY PROPERTIES ARISING FROM ASYMPTOTIC COMPLETENESS IN QUANTUM FIELD THEORY.pdf},
         pages = {99},
         slaccitation = {\%\%CITATION = CMPHA,80,99\\;\%\%},
         title = {{SOME ANALYTICITY PROPERTIES ARISING FROM ASYMPTOTIC COMPLETENESS IN QUANTUM FIELD THEORY}},
         volume = {80},
         year = {1981}
 }
 
 @article{Emch:1981,
         author = {G. G. Emch},
         journal = {Int. J. Theor. Phys.},
         localfile = {1981 - Emch - Prequantization and KMS structures.pdf},
         pages = {891--904},
         slaccitation = {\%\%CITATION = IJTPB,20,891\\;\%\%},
         title = {{PREQUANTIZATION AND KMS STRUCTURES}},
         volume = {20},
         year = {1981}
 }
 
 @article{Buchholz:1982,
         author = {D. Buchholz},
         journal = {Commun. Math. Phys.},
         localfile = {1982 - Buchholz - THE PHYSICAL STATE SPACE OF QUANTUM ELECTRODYNAMICS.pdf},
         pages = {49},
         slaccitation = {\%\%CITATION = CMPHA,85,49\\;\%\%},
         title = {{THE PHYSICAL STATE SPACE OF QUANTUM ELECTRODYNAMICS}},
         volume = {85},
         year = {1982}
 }
 
 @article{HislopLongo:1982,
         author = {P. D. Hislop and R. Longo},
         journal = {Commun. Math. Phys.},
         localfile = {1982 - Hislop, Longo - Modular structure of the local algebras associated with the free massless scalar field theory.pdf},
         pages = {71},
         slaccitation = {\%\%CITATION = CMPHA,84,71\\;\%\%},
         title = {{Modular Structure of the Local Algebras Associated with the Free Massless Scalar Field Theory}},
         volume = {84},
         year = {1982}
 }
 
 @article{Steinmann:1982,
         author = {O. Steinmann},
         journal = {Commun. Math. Phys.},
         localfile = {1982 - Steinmann - A JOST-SCHROER THEOREM FOR STRING FIELDS.pdf},
         pages = {259},
         slaccitation = {\%\%CITATION = CMPHA,87,259\\;\%\%},
         title = {{A {J}OST-{S}CHROER THEOREM FOR STRING FIELDS}},
         volume = {87},
         year = {1982}
 }
 
 @article{DoplicherLongo:1983,
         author = {S. Doplicher and R. Longo},
         journal = {Commun. Math. Phys.},
         localfile = {1983 - Doplicher, Longo - LOCAL ASPECTS OF SUPERSELECTION RULES. II.pdf},
         pages = {399--409},
         slaccitation = {\%\%CITATION = CMPHA,88,399\\;\%\%},
         title = {{Local Aspects of Superselection Rules II}},
         volume = {88},
         year = {1983}
 }
 
 @article{Wichmann:1983,
         author = {E. H. Wichmann},
         journal = {J. Math. Phys.},
         localfile = {1983 - Wichmann - ON SYSTEMS OF LOCAL OPERATORS AND THE DUALITY CONDITION.pdf},
         pages = {1633--1644},
         slaccitation = {\%\%CITATION = JMAPA,24,1633\\;\%\%},
         title = {{ON SYSTEMS OF LOCAL OPERATORS AND THE DUALITY CONDITION}},
         volume = {24},
         year = {1983}
 }
 
 @article{BaumgrtelWollenberg:1984,
         author = {H. Baumg{\"{a}}rtel and M. Wollenberg},
         journal = {Commun. Math. Phys.},
         localfile = {1984 - Baumg\"{a}rtel, Wollenberg - A class of nontrivial weakly local massive Wightman fields with interpolating properties.pdf},
         pages = {331--352},
         slaccitation = {\%\%CITATION = CMPHA,94,331\\;\%\%},
         title = {{A CLASS OF NONTRIVIAL WEAKLY LOCAL MASSIVE {W}IGHTMAN FIELDS WITH INTERPOLATING PROPERTIES}},
         volume = {94},
         year = {1984}
 }
 
 @article{Borchers:1984,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Commun. Math. Phys.},
         localfile = {1984 - Borchers - Translation Group and Spectrum Condition.pdf},
         pages = {1--13},
         title = {{Translation group and Spectrum Condition}},
         volume = {96},
         year = {1984}
 }
 
 @article{BorchersBuchholz:1985,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and D. Buchholz},
         journal = {Commun. Math. Phys.},
         localfile = {1985 - Borchers, Buchholz - The Energy-Momentum Spectrum in Local Field Theories with Broken Lorentz-Symmetry.pdf},
         pages = {169},
         slaccitation = {\%\%CITATION = CMPHA,97,169\\;\%\%},
         title = {{THE ENERGY MOMENTUM SPECTRUM IN LOCAL FIELD THEORIES WITH BROKEN LORENTZ SYMMETRY}},
         volume = {97},
         year = {1985}
 }
 
 @article{BuchholzEpstein:1985,
         author = {D. Buchholz and H. Epstein},
         journal = {Fizika},
         localfile = {1985 - Buchholz, Epstein - Spin and Statistics of Quantum Topological Charges.pdf},
         pages = {329},
         slaccitation = {\%\%CITATION = FZKAA,17,329\\;\%\%},
         title = {{SPIN AND STATISTICS OF QUANTUM TOPOLOGICAL CHARGES}},
         volume = {17},
         year = {1985}
 }
 
 @article{BuchholzJunglas:1986,
         author = {D. Buchholz and P. Junglas},
         journal = {Lett. Math. Phys.},
         localfile = {1986 - Buchholz, Junglas - LOCAL PROPERTIES OF EQUILIBRIUM STATES AND THE PARTICLE SPECTRUM IN QUANTUM FIELD THEORY.pdf},
         pages = {51},
         slaccitation = {\%\%CITATION = LMPHD,11,51\\;\%\%},
         title = {{LOCAL PROPERTIES OF EQUILIBRIUM STATES AND THE PARTICLE SPECTRUM IN QUANTUM FIELD THEORY}},
         volume = {11},
         year = {1986}
 }
 
 @article{DriesslerSummersWichmann:1986,
         author = {W. Driessler and S. J. Summers and E. H. Wichmann},
         doi = {10.1007/BF01212341},
         journal = {Commun. Math. Phys.},
         localfile = {1986 - Driessler, Summers, Wichmann - On the connection between quantum fields and von Neumann algebras of local operators.pdf},
         pages = {49--84},
         slaccitation = {\%\%CITATION = CMPHA,105,49\\;\%\%},
         title = {{On the Connection between Quantum Fields and von Neumann Algebras of Local Operators}},
         volume = {105},
         year = {1986}
 }
 
 @article{PohlmeyerRehren:1986,
         author = {K. Pohlmeyer and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         journal = {Commun. Math. Phys.},
         localfile = {1986 - Pohlmeyer, Rehren - ALGEBRAIC PROPERTIES OF THE INVARIANT CHARGES OF THE NAMBU- GOTO THEORY.pdf},
         pages = {593},
         slaccitation = {\%\%CITATION = CMPHA,105,593\\;\%\%},
         title = {{ALGEBRAIC PROPERTIES OF THE INVARIANT CHARGES OF THE NAMBU- GOTO THEORY}},
         volume = {105},
         year = {1986}
 }
 
 @article{BuchholzFredenhagenDAntoni:1987,
         author = {D. Buchholz and K. Fredenhagen and C. D'Antoni},
         journal = {Commun. Math. Phys.},
         localfile = {1987 - Buchholz, D'Antoni, Fredenhagen - The universal structure of local algebras.pdf},
         pages = {123},
         slaccitation = {\%\%CITATION = CMPHA,111,123\\;\%\%},
         title = {{The universal structure of local algebras}},
         volume = {111},
         year = {1987}
 }
 
 @article{BuchholzJacobi:1987,
         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.},
         author = {D. Buchholz and P. Jacobi},
         journal = {Lett. Math. Phys.},
         localfile = {1987 - Buchholz, Jacobi - On the Nuclearity Condition for Massless Fields.pdf},
         pages = {313},
         slaccitation = {\%\%CITATION = LMPHD,13,313\\;\%\%},
         title = {{On the Nuclearity Condition for Massless Fields}},
         volume = {13},
         year = {1987}
 }
 
 @article{PohlmeyerRehren:1988-1,
         author = {K. Pohlmeyer and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         journal = {Commun. Math. Phys.},
         localfile = {1988 - Pohlmeyer, Rehren - THE ALGEBRA FORMED BY THE INVARIANT CHARGES OF THE NAMBU- GOTO THEORY: IDENTIFICATION OF A MAXIMAL ABELIAN SUBALGEBRA.pdf},
         pages = {55},
         slaccitation = {\%\%CITATION = CMPHA,114,55\\;\%\%},
         title = {{THE ALGEBRA FORMED BY THE INVARIANT CHARGES OF THE NAMBU- GOTO THEORY: IDENTIFICATION OF A MAXIMAL ABELIAN SUBALGEBRA}},
         volume = {114},
         year = {1988}
 }
 
 @article{PohlmeyerRehren:1988,
         author = {K. Pohlmeyer and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         journal = {Commun. Math. Phys.},
         localfile = {1988 - Pohlmeyer, Rehren - THE INVARIANT CHARGES OF THE NAMBU-GOTO THEORY: THEIR GEOMETRIC ORIGIN AND THEIR COMPLETENESS.pdf},
         pages = {177},
         slaccitation = {\%\%CITATION = CMPHA,114,177\\;\%\%},
         title = {{THE INVARIANT CHARGES OF THE NAMBU-GOTO THEORY: THEIR GEOMETRIC ORIGIN AND THEIR COMPLETENESS}},
         volume = {114},
         year = {1988}
 }
 
 @article{BuchholzJunglas:1989,
         author = {D. Buchholz and P. Junglas},
         journal = {Commun. Math. Phys.},
         localfile = {1989 - Buchholz, Junglas - On the existence of equilibrium states in local quantum field theory.pdf},
         pages = {255--270},
         slaccitation = {\%\%CITATION = CMPHA,121,255\\;\%\%},
         title = {{ON THE EXISTENCE OF EQUILIBRIUM STATES IN LOCAL QUANTUM FIELD THEORY}},
         volume = {121},
         year = {1989}
 }
 
 @article{Borchers:1990,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Commun. Math. Phys.},
         localfile = {1990 - Borchers - Translation group and modular automorphisms for local regions.pdf},
         pages = {189--200},
         slaccitation = {\%\%CITATION = CMPHA,132,189\\;\%\%},
         title = {{Translation group and modular automorphisms for local regions}},
         volume = {132},
         year = {1990}
 }
 
 @article{BorchersYngvason:1990,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and J. Yngvason},
         doi = {10.1007/BF02104505},
         journal = {Commun. Math. Phys.},
         localfile = {1990 - Borchers, Yngvason - Positivity of Wightman functionals and the existence of local nets.pdf},
         pages = {607},
         slaccitation = {\%\%CITATION = CMPHA,127,607\\;\%\%},
         title = {{Positivity of Wightman functionals and the existence of local nets}},
         url = {http://projecteuclid.org/euclid.cmp/1104180223},
         volume = {127},
         year = {1990}
 }
 
 @article{Rehren:1990,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         journal = {Commun. Math. Phys.},
         localfile = {1990 - Rehren - SPACE-TIME FIELDS AND EXCHANGE FIELDS.pdf},
         pages = {461--484},
         slaccitation = {\%\%CITATION = CMPHA,132,461\\;\%\%},
         title = {{SPACE-TIME FIELDS AND EXCHANGE FIELDS}},
         volume = {132},
         year = {1990}
 }
 
 @article{BorchersWollenberg:1991,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and M. Wollenberg},
         journal = {Commun. Math. Phys.},
         localfile = {1991 - Borchers, Wollenberg - On the relation between types of local algebras in different global representations.pdf},
         pages = {161--174},
         slaccitation = {\%\%CITATION = CMPHA,137,161\\;\%\%},
         title = {{On the relation between types of local algebras in different global representations}},
         volume = {137},
         year = {1991}
 }
 
 @article{KayWald:1991,
         author = {B. S. Kay and R. M. Wald},
         journal = {Phys. Rept.},
         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},
         pages = {49--136},
         slaccitation = {\%\%CITATION = PRPLC,207,49\\;\%\%},
         title = {{Theorems on the Uniqueness and Thermal Properties of Stationary, Nonsingular, Quasifree States on Space-Times with a Bifurcate Killing Horizon}},
         volume = {207},
         year = {1991}
 }
 
 @article{AshtekarIsham:1992,
         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.},
         author = {A. Ashtekar and C. J. Isham},
         eprint = {hep-th/9202053},
         journal = {Class. Quant. Grav.},
         localfile = {1992 - Ashtekar, Isham - Representations of the holonomy algebras of gravity and non-Abelian gauge theories.pdf},
         pages = {1433--1468},
         slaccitation = {\%\%CITATION = HEP-TH/9202053\\;\%\%},
         title = {{Representations of the holonomy algebras of gravity and nonAbelian gauge theories}},
         url = {http://arxiv.org/abs/hep-th/9202053},
         volume = {9},
         year = {1992}
 }
 
 @article{BuchholzWanzenberg:1992,
         author = {D. Buchholz and R. Wanzenberg},
         journal = {Commun. Math. Phys.},
         localfile = {1992 - Buchholz, Wanzenberg - The realm of the vacuum.pdf},
         pages = {577--590},
         slaccitation = {\%\%CITATION = CMPHA,143,577\\;\%\%},
         title = {{The Realm of the vacuum}},
         volume = {143},
         year = {1992}
 }
 
 @article{Kay:1993,
         author = {B. S. Kay},
         journal = {J. Math. Phys.},
         localfile = {1993 - Kay - Sufficient conditions for quasifree states and an improved uniqueness theorem for quantum fields on space-times with horizons.pdf},
         pages = {4519--4539},
         slaccitation = {\%\%CITATION = JMAPA,34,4519\\;\%\%},
         title = {{Sufficient conditions for quasifree states and an improved uniqueness theorem for quantum fields on space-times with horizons}},
         volume = {34},
         year = {1993}
 }
 
 @article{Rehren:1992,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         journal = {Commun. Math. Phys.},
         localfile = {1992 - Rehren - Field operators for anyons and plektons.pdf},
         pages = {123--148},
         slaccitation = {\%\%CITATION = CMPHA,145,123\\;\%\%},
         title = {{Field operators for anyons and plektons}},
         volume = {145},
         year = {1992}
 }
 
 @article{Thirring:1992,
         author = {W. Thirring},
         localfile = {1992 - Thirring - Ergodic Properties in Quantum Systems.pdf},
         note = {UWTHPH-1992-6},
         title = {{Ergodic properties in quantum systems}},
         year = {1992}
 }
 
 @article{BrunettiGuidoLongo:1993,
         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.},
         author = {R. Brunetti and D. Guido and R. Longo},
         eprint = {funct-an/9302008},
         journal = {Commun. Math. Phys.},
         localfile = {1993 - Brunetti, Guido, Longo - Modular Structure and Duality in Conformal Quantum Field Theory.pdf},
         pages = {201--220},
         slaccitation = {\%\%CITATION = FUNCT-AN/9302008\\;\%\%},
         title = {{Modular structure and duality in conformal quantum field theory}},
         url = {http://arxiv.org/abs/funct-an/9302008},
         volume = {156},
         year = {1993}
 }
 
 @article{BuchholzDoplicherLongoRoberts:1993,
         author = {D. Buchholz and S. Doplicher and R. Longo and J. E. Roberts},
         journal = {Commun. Math. Phys.},
         localfile = {1993 - Buchholz, Doplicher, Longo, Roberts - Extensions of automorphisms and gauge symmetries.pdf},
         pages = {123--134},
         slaccitation = {\%\%CITATION = CMPHA,155,123\\;\%\%},
         title = {{Extensions of automorphisms and gauge symmetries}},
         volume = {155},
         year = {1993}
 }
 
 @article{FringMussardoSimonetti:1993,
         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.},
         author = {A. Fring and G. Mussardo and P. Simonetti},
         eprint = {hep-th/9303108},
         journal = {Phys. Lett.},
         localfile = {1993 - Fring, Mussardo, Simonetti - Form Factors of the Elementary Field in the Bullough-Dodd Model.pdf},
         pages = {83--90},
         slaccitation = {\%\%CITATION = HEP-TH/9303108\\;\%\%},
         title = {{Form-factors of the elementary field in the Bullough-Dodd model}},
         url = {http://arxiv.org/abs/hep-th/9303108},
         volume = {B307},
         year = {1993}
 }
 
 @article{BuchholzYngvason:1994,
         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.},
         author = {D. Buchholz and J. Yngvason},
         eprint = {hep-th/9403027},
         journal = {Phys. Rev. Lett.},
         localfile = {1994 - Buchholz, Yngvason - There are no causality problems for Fermis Two Atom System.pdf},
         pages = {613--616},
         slaccitation = {\%\%CITATION = HEP-TH/9403027\\;\%\%},
         title = {{There are no causality problems for Fermi's two atom system}},
         url = {http://arxiv.org/abs/hep-th/9403027},
         volume = {73},
         year = {1994}
 }
 
 @article{DoplicherFredenhagenRoberts:1995,
         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.},
         author = {S. Doplicher and K. Fredenhagen and J. E. Roberts},
         eprint = {hep-th/0303037},
         journal = {Commun. Math. Phys.},
         localfile = {1994 - Doplicher, Fredenhagen, Roberts - The Quantum Structure of Spacetime at the Planck Scale and Quantum Fields.pdf},
         pages = {187--220},
         slaccitation = {\%\%CITATION = HEP-TH/0303037\\;\%\%},
         title = {{The Quantum structure of space-time at the {P}lanck scale and quantum fields}},
         url = {http://arxiv.org/abs/hep-th/0303037},
         volume = {172},
         year = {1995}
 }
 
 @article{Lashkevich:1994,
         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.},
         author = {M. Yu. Lashkevich},
         eprint = {hep-th/9406118},
         localfile = {1994 - Lashkevich - Sectors of mutually local fields in integrable models of quantum field theory.pdf},
         slaccitation = {\%\%CITATION = HEP-TH/9406118\\;\%\%},
         title = {{Sectors of mutually local fields in integrable models of quantum field theory}},
         url = {http://arxiv.org/abs/hep-th/9406118},
         year = {1994}
 }
 
 @article{Smirnov:1994,
         abstract = {Some mistaken reasonings at the end of the paper omitted.},
         author = {F. A. Smirnov},
         eprint = {hep-th/9312039},
         journal = {Int. J. Mod. Phys.},
         localfile = {1994 - Smirnov - A New set of exact form-factors.pdf},
         pages = {5121--5144},
         slaccitation = {\%\%CITATION = HEP-TH/9312039\\;\%\%},
         title = {{A New set of exact form-factors}},
         url = {http://arxiv.org/abs/hep-th/9312039},
         volume = {A9},
         year = {1994}
 }
 
 @article{Verch:1994,
         author = {R. Verch},
         journal = {Commun. Math. Phys.},
         localfile = {1994 - Verch - Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved spacetime.pdf},
         pages = {507--536},
         slaccitation = {\%\%CITATION = CMPHA,160,507\\;\%\%},
         title = {{Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved space-time}},
         volume = {160},
         year = {1994}
 }
 
 @article{Borchers:1995,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Annales Poincare Phys. Theor.},
         localfile = {1995 - Borchers - On the use of modular groups in quantum field theory.pdf},
         pages = {331--382},
         slaccitation = {\%\%CITATION = AHPAA,63,331\\;\%\%},
         title = {{On the use of modular groups in quantum field theory}},
         volume = {63},
         year = {1995}
 }
 
 @article{LiguoriMintchev:1995-1,
         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.},
         author = {A. Liguori and M. Mintchev},
         eprint = {hep-th/9403039},
         journal = {Commun. Math. Phys.},
         localfile = {1995 - Liguori, Mintchev - Fock representations of quantum fields with generalized statistics.pdf},
         pages = {635--652},
         slaccitation = {\%\%CITATION = HEP-TH/9403039\\;\%\%},
         title = {{Fock representations of quantum fields with generalized statistics}},
         url = {http://arxiv.org/abs/hep-th/9403039},
         volume = {169},
         year = {1995}
 }
 
 @article{LiguoriMintchevRossi:1995,
         author = {A. Liguori and M. Mintchev and M. Rossi},
         journal = {Lett. Math. Phys.},
         localfile = {1995 - Liguori, Mintchev, Rossi - Unitary Group Representations in Fock Spaces with Generalized Exchange Properties.pdf},
         pages = {163--177},
         slaccitation = {\%\%CITATION = LMPHD,35,163\\;\%\%},
         title = {{Unitary group representations in Fock spaces with generalized exchange properties}},
         volume = {35},
         year = {1995}
 }
 
 @article{FlorigSummers:1997,
         author = {M. Florig and S. J. Summers},
         journal = {J. Math. Phys.},
         localfile = {1996 - Florig, Summers - On the statistical independence of algebras of observables.pdf},
         pages = {1318--1328},
         slaccitation = {\%\%CITATION = JMAPA,38,1318\\;\%\%},
         title = {{On the statistical independence of algebras of observables}},
         volume = {38},
         year = {1997}
 }
 
 @article{Jr:1996,
         abstract = {Starting from a conformal Haag-Kastler net in 1+1 dimensions, Wightman functions are constructed.},
         author = {M. J{\"{o}}r{\ss}},
         eprint = {hep-th/9609020},
         localfile = {1996 - Jorss - From conformal Haag-Kastler nets to Wightman functions.pdf},
         slaccitation = {\%\%CITATION = HEP-TH/9609020\\;\%\%},
         title = {{From conformal Haag-Kastler nets to Wightman functions}},
         url = {http://arxiv.org/abs/hep-th/9609020},
         year = {1996}
 }
 
 @article{Rehren:1996,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         journal = {Commun. Math. Phys.},
         localfile = {1996 - Rehren - Comments on a recent solution to Wightman's axioms.pdf},
         pages = {453--466},
         slaccitation = {\%\%CITATION = CMPHA,178,453\\;\%\%},
         title = {{Comments on a recent solution to Wightman's axioms}},
         volume = {178},
         year = {1996}
 }
 
 @article{RehrenStanevTodorov:1995,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren and Y. S. Stanev and I. T. Todorov},
         eprint = {hep-th/9409165},
         journal = {Commun. Math. Phys.},
         localfile = {1995 - Rehren, Stanev, TodorovIvan T - Characterizing invariants for local extensions of current algebras.pdf},
         pages = {605--634},
         slaccitation = {\%\%CITATION = HEP-TH/9409165\\;\%\%},
         title = {{Characterizing invariants for local extensions of current algebras}},
         url = {http://arxiv.org/abs/hep-th/9409165},
         volume = {174},
         year = {1995}
 }
 
 @article{Schroer:1997-2,
         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.},
         author = {B. Schroer},
         eprint = {hep-th/9608083},
         journal = {Annals Phys.},
         localfile = {1997 - Schroer - Motivations and physical aims of algebraic QFT.pdf},
         pages = {270--304},
         slaccitation = {\%\%CITATION = HEP-TH/9608083\\;\%\%},
         title = {{Motivations and physical aims of algebraic QFT}},
         url = {http://arxiv.org/abs/hep-th/9608083},
         volume = {255},
         year = {1997}
 }
 
 @article{Schumann:1996,
         author = {R. Schumann},
         journal = {Lett. Math. Phys.},
         localfile = {1996 - Schumann - Operator Ideals and the Statistical Independence in Quantum Field Theory.pdf},
         pages = {249--271},
         slaccitation = {\%\%CITATION = LMPHD,37,249\\;\%\%},
         title = {{Operator ideals and the statistical independence in quantum field theory}},
         volume = {37},
         year = {1996}
 }
 
 @article{Yngvason:1996,
         author = {J. Yngvason},
         journal = {Annales Poincare Phys. Theor.},
         localfile = {1996 - Yngvason - Tomita Conjugations and Transitivity of Locality.pdf},
         pages = {395--408},
         slaccitation = {\%\%CITATION = AHPAA,64,395\\;\%\%},
         title = {{Tomita conjugations and transitivity of locality}},
         volume = {64},
         year = {1996}
 }
 
 @article{LiguoriMintchevRossi:1997,
         author = {A. Liguori and M. Mintchev and M. Rossi},
         journal = {J. Math. Phys.},
         localfile = {1997 - Liguori, Mintchev, Rossi - Fock representations of exchange algebras with involution.pdf},
         pages = {2888--2898},
         slaccitation = {\%\%CITATION = JMAPA,38,2888\\;\%\%},
         title = {{Fock representations of exchange algebras with involution}},
         volume = {38},
         year = {1997}
 }
 
 @article{Niedermaier:1998,
         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.},
         author = {M. R. Niedermaier},
         eprint = {hep-th/9706172},
         journal = {Commun. Math. Phys.},
         localfile = {1997 - Niedermaier - A Derivation of the Cyclic Form Factor Equation.pdf},
         pages = {411--428},
         slaccitation = {\%\%CITATION = HEP-TH/9706172\\;\%\%},
         title = {{A derivation of the cyclic form factor equation}},
         url = {http://arxiv.org/abs/hep-th/9706172},
         volume = {196},
         year = {1998}
 }
 
 @article{Rehren:1998,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         eprint = {hep-th/9711085},
         journal = {Lett. Math. Phys.},
         localfile = {1998 - Rehren - Spin statistics and CPT for solitons.pdf},
         pages = {95--110},
         slaccitation = {\%\%CITATION = HEP-TH/9711085\\;\%\%},
         title = {{Spin statistics and CPT for solitons}},
         url = {http://arxiv.org/abs/hep-th/9711085},
         volume = {46},
         year = {1998}
 }
 
 @article{ThomasWichmann:1997,
         author = {L. J. Thomas and E. H. Wichmann},
         doi = {10.1063/1.531954},
         journal = {J. Math. Phys.},
         localfile = {1997 - Thomas, Wichmann - On the Causal Structure of Minkowski Spacetime.pdf},
         pages = {5044--5086},
         slaccitation = {\%\%CITATION = JMAPA,38,5044\\;\%\%},
         title = {{On the causal structure of {M}inkowski space-time}},
         volume = {38},
         year = {1997}
 }
 
 @article{BuchholzDreyerFlorigSummers:2000,
         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.},
         author = {D. Buchholz and O. Dreyer and M. Florig and S. J. Summers},
         eprint = {math-ph/9805026},
         journal = {Rev. Math. Phys.},
         localfile = {1998 - Buchholz, Dreyer, Florig, Summers - Geometric modular action and spacetime symmetry groups.pdf},
         pages = {475--560},
         slaccitation = {\%\%CITATION = MATH-PH/9805026\\;\%\%},
         title = {{Geometric modular action and spacetime symmetry groups}},
         url = {http://arxiv.org/abs/math-ph/9805026},
         volume = {12},
         year = {2000}
 }
 
 @article{FlorigSummers:2000,
         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.},
         author = {M. Florig and S. J. Summers},
         eprint = {math-ph/0006011},
         journal = {Proc. Lond. Math. Soc.},
         localfile = {2000 - Florig, Summers - Further representations of the canonical commutation relations.pdf},
         pages = {451--490},
         slaccitation = {\%\%CITATION = MATH-PH/0006011\\;\%\%},
         title = {{Further representations of the canonical commutation relations}},
         url = {http://arxiv.org/abs/math-ph/0006011},
         volume = {80},
         year = {2000}
 }
 
 @article{SchroerWiesbrock:2000-1,
         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.},
         author = {B. Schroer and H.W. Wiesbrock},
         eprint = {hep-th/9812251},
         journal = {Rev. Math. Phys.},
         localfile = {1998 - Schroer, Wiesbrock - Modular constructions of quantum field theories with interactions.pdf},
         pages = {301--326},
         slaccitation = {\%\%CITATION = HEP-TH/9812251\\;\%\%},
         title = {{Modular constructions of quantum field theories with interactions}},
         url = {http://arxiv.org/abs/hep-th/9812251},
         volume = {12},
         year = {2000}
 }
 
 @article{ThomasWichmann:1998,
         author = {L. J. Thomas and E. H. Wichmann},
         journal = {J. Math. Phys.},
         localfile = {1998 - Thomas, Wichmann - Standard Forms of local nets in quantum field theory.pdf},
         pages = {2643--2681},
         slaccitation = {\%\%CITATION = JMAPA,39,2643\\;\%\%},
         title = {{Standard forms of local nets in quantum field theory}},
         volume = {39},
         year = {1998}
 }
 
 @article{BabujianKarowski:1999,
         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.},
         author = {H. M. Babujian and M. Karowski},
         eprint = {hep-th/9909153},
         journal = {Phys. Lett.},
         localfile = {1999 - Babujian, Karowski - The Exact Quantum Sine-Gordon Field Equation and Other Non-Perturbative Results.pdf},
         pages = {53--57},
         slaccitation = {\%\%CITATION = HEP-TH/9909153\\;\%\%},
         title = {{The exact quantum sine-Gordon field equation and other non- perturbative results}},
         url = {http://arxiv.org/abs/hep-th/9909153},
         volume = {B471},
         year = {1999}
 }
 
 @article{Fewster:2000,
         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.},
         author = {C. J. Fewster},
         eprint = {gr-qc/9910060},
         journal = {Class. Quant. Grav.},
         localfile = {2000 - Fewster - A general worldline quantum inequality.pdf},
         pages = {1897--1911},
         slaccitation = {\%\%CITATION = GR-QC/9910060\\;\%\%},
         title = {{A general worldline quantum inequality}},
         url = {http://arxiv.org/abs/gr-qc/9910060},
         volume = {17},
         year = {2000}
 }
 
 @article{FewsterTeo:1999,
         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.},
         author = {C. J. Fewster and E. Teo},
         eprint = {gr-qc/9812032},
         journal = {Phys. Rev.},
         localfile = {1999 - Fewster, Teo - Bounds on negative energy densities in static space-times.pdf},
         pages = {104016},
         slaccitation = {\%\%CITATION = GR-QC/9812032\\;\%\%},
         title = {{Bounds on negative energy densities in static space-times}},
         url = {http://arxiv.org/abs/gr-qc/9812032},
         volume = {D59},
         year = {1999}
 }
 
 @article{GaierYngvason:2000,
         author = {J. Gaier and J. Yngvason},
         journal = {J. Math. Phys.},
         localfile = {1999 - Gaier, Yngvason - Geometric Modular Action, Wedge Duality and Lorentz Covariance are Equivalent for Generalized Free Fields.pdf},
         pages = {5910--5919},
         slaccitation = {\%\%CITATION = JMAPA,41,5910\\;\%\%},
         title = {{Geometric modular action, wedge duality, and Lorentz covariance are equivalent for generalized free fields}},
         volume = {41},
         year = {2000}
 }
 
 @article{GuidoLongoRobertsVerch:2001,
         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).},
         author = {D. Guido and R. Longo and J. E. Roberts and R. Verch},
         doi = {10.1142/S0129055X01000557},
         eprint = {math-ph/9906019},
         journal = {Rev. Math. Phys.},
         localfile = {1999 - Guido, Longo, Roberts, Verch - Charged sectors, spin and statistics in quantum field theory on curved spacetimes.pdf},
         pages = {125--198},
         slaccitation = {\%\%CITATION = MATH-PH/9906019\\;\%\%},
         title = {{Charged sectors, spin and statistics in quantum field theory on curved spacetimes}},
         url = {http://arxiv.org/abs/math-ph/9906019},
         volume = {13},
         year = {2001}
 }
 
 @article{Rainer:1999,
         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.},
         author = {M. Rainer},
         eprint = {gr-qc/9912011},
         localfile = {1999 - Rainer - Is loop quantum gravity a QFT?.pdf},
         slaccitation = {\%\%CITATION = GR-QC/9912011\\;\%\%},
         title = {{Is loop quantum gravity a QFT?}},
         url = {http://arxiv.org/abs/gr-qc/9912011},
         year = {1999}
 }
 
 @article{Borchers:2000,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {J. Math. Phys.},
         localfile = {2000 - Borchers - On Revolutionizing Quantum Field Theory.pdf},
         pages = {3604--3673},
         slaccitation = {\%\%CITATION = JMAPA,41,3604\\;\%\%},
         title = {{On revolutionizing quantum field theory with Tomita's modular theory}},
         volume = {41},
         year = {2000}
 }
 
 @article{BuchholzDoplicherMorchioRobertsStrocchi:2001,
         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.},
         author = {D. Buchholz and S. Doplicher and G. Morchio and J. E. Roberts and F. Strocchi},
         eprint = {hep-th/0011015},
         journal = {Ann. Phys.},
         localfile = {2000 - Buchholz, Doplicher, Morchio, Roberts, Strocchi - Quantum Delocalization of the Electric Charge.pdf},
         pages = {53--66},
         slaccitation = {\%\%CITATION = HEP-TH/0011015\\;\%\%},
         title = {{Quantum delocalization of the electric charge}},
         url = {http://arxiv.org/abs/hep-th/0011015},
         volume = {290},
         year = {2001}
 }
 
 @article{BuchholzMundSummers:2001,
         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.},
         author = {D. Buchholz and J. Mund and S. J. Summers},
         eprint = {hep-th/0011237},
         journal = {Fields Inst. Commun.},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2000 - Buchholz, Mund, Summers - Transplantation of Local Nets and Geometric Modular Action on Robertson-Walker Space-Times.pdf},
         pages = {65--81},
         pdf = {http://arxiv.org/pdf/hep-th/0011237},
         slaccitation = {\%\%CITATION = HEP-TH/0011237\\;\%\%},
         title = {{Transplantation of Local Nets and Geometric Modular Action on Robertson-Walker Space-Times}},
         url = {http://arxiv.org/abs/hep-th/0011237},
         v1descr = {Mon, 27 Nov 2000 14:07:33 GMT (23kb)},
         v2descr = {Fri, 15 Dec 2000 13:00:27 GMT (23kb)},
         volume = {30},
         year = {2001}
 }
 
 @article{Fleischhack:2000,
         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.},
         author = {C. Fleischhack},
         eprint = {math-ph/0001006},
         journal = {Commun. Math. Phys.},
         localfile = {2000 - Fleischhack - Gauge Orbit Types for Generalized Connections.pdf},
         pages = {607--649},
         slaccitation = {\%\%CITATION = MATH-PH/0001006\\;\%\%},
         title = {{Gauge Orbit Types for Generalized Connections}},
         url = {http://arxiv.org/abs/math-ph/0001006},
         volume = {214},
         year = {2000}
 }
 
 @article{Fleischhack:2000-1,
         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.},
         author = {C. Fleischhack},
         eprint = {math-ph/0001007},
         localfile = {2000 - Fleischhack - Hyphs and the Ashtekar-Lewandowski measure.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0001007\\;\%\%},
         title = {{Hyphs and the Ashtekar-Lewandowski measure}},
         url = {http://arxiv.org/abs/math-ph/0001007},
         year = {2000}
 }
 
 @article{Fleischhack:2000-2,
         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.},
         author = {C. Fleischhack},
         eprint = {math-ph/0001008},
         localfile = {2000 - Fleischhack - Stratification of the Generalized Gauge Orbit Space.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0001008\\;\%\%},
         title = {{Stratification of the Generalized Gauge Orbit Space}},
         url = {http://arxiv.org/abs/math-ph/0001008},
         year = {2000}
 }
 
 @article{Oeckl:2000,
         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.},
         author = {R. Oeckl},
         eprint = {hep-th/0003018},
         journal = {Nucl. Phys.},
         localfile = {2000 - Oeckl - Untwisting noncommutative R**d and the equivalence of quantum field theories.pdf},
         pages = {559--574},
         slaccitation = {\%\%CITATION = HEP-TH/0003018\\;\%\%},
         title = {{Untwisting noncommutative R**d and the equivalence of quantum field theories}},
         url = {http://arxiv.org/abs/hep-th/0003018},
         volume = {B581},
         year = {2000}
 }
 
 @article{Ramacher:2000,
         author = {P. Ramacher},
         journal = {J. Math. Phys.},
         localfile = {2000 - Ramacher - Modular localization of elementary systems in the theory of Wigner.pdf},
         pages = {6079--6089},
         slaccitation = {\%\%CITATION = JMAPA,41,6079\\;\%\%},
         title = {{Modular localization of elementary systems in the theory of Wigner}},
         volume = {41},
         year = {2000}
 }
 
 @article{DtschFredenhagen:2001-1,
         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.},
         author = {M. D{\"{u}}tsch and K. Fredenhagen},
         eprint = {hep-th/0001129},
         journal = {Commun. Math. Phys.},
         localfile = {2001 - D\"{u}tsch, Fedenhagen - Perturbative Algebraic Field Theory, and Deformation Quantization.pdf},
         pages = {5--30},
         slaccitation = {\%\%CITATION = HEP-TH/0001129\\;\%\%},
         title = {{Algebraic quantum field theory, perturbation theory, and the loop expansion}},
         url = {http://arxiv.org/abs/hep-th/0001129},
         volume = {219},
         year = {2001}
 }
 
 @article{FassarellaSchroer:2001,
         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.},
         author = {L. Fassarella and B. Schroer},
         eprint = {hep-th/0106064},
         localfile = {2001 - Fassarella, Schroer - The fuzzy analog of chiral diffeomorphisms in higher dimensional quantum field theories.pdf},
         slaccitation = {\%\%CITATION = HEP-TH/0106064\\;\%\%},
         title = {{The fuzzy analog of chiral diffeomorphisms in higher dimensional quantum field theories}},
         url = {http://arxiv.org/abs/hep-th/0106064},
         year = {2001}
 }
 
 @article{FewsterVerch:2002,
         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.},
         author = {C. J. Fewster and R. Verch},
         doi = {10.1007/s002200100584},
         eprint = {math-ph/0105027},
         journal = {Commun. Math. Phys.},
         localfile = {2001 - Fewster, Verch - A Quantum weak energy inequality for Dirac fields in curved space-time.pdf},
         pages = {331--359},
         slaccitation = {\%\%CITATION = MATH-PH/0105027\\;\%\%},
         title = {{A quantum weak energy inequality for Dirac fields in curved spacetime}},
         url = {http://arxiv.org/abs/math-ph/0105027},
         volume = {225},
         year = {2002}
 }
 
 @article{FleischhackLewandowski:2001,
         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.},
         author = {C. Fleischhack and J. Lewandowski},
         eprint = {math-ph/0111001},
         localfile = {2001 - Fleischhack, Lewandowski - Breakdown of the action method in gauge theories.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0111001\\;\%\%},
         title = {{Breakdown of the action method in gauge theories}},
         url = {http://arxiv.org/abs/math-ph/0111001},
         year = {2001}
 }
 
 @article{Fleischhack:2003-1,
         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.},
         author = {C. Fleischhack},
         eprint = {math-ph/0007001},
         journal = {Commun. Math. Phys.},
         localfile = {2003 - Fleischhack - On the Gribov problem for generalized connections.pdf},
         pages = {423--454},
         slaccitation = {\%\%CITATION = MATH-PH/0007001\\;\%\%},
         title = {{On the Gribov problem for generalized connections}},
         url = {http://arxiv.org/abs/math-ph/0007001},
         volume = {234},
         year = {2003}
 }
 
 @article{Fleischhack:2001,
         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.},
         author = {C. Fleischhack},
         eprint = {math-ph/0107022},
         localfile = {2001 - Fleischhack - On the structure of physical measures in gauge theories.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0107022\\;\%\%},
         title = {{On the structure of physical measures in gauge theories}},
         url = {http://arxiv.org/abs/math-ph/0107022},
         year = {2001}
 }
 
 @article{Fleischhack:2001-1,
         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.},
         author = {C. Fleischhack},
         eprint = {math-ph/0109030},
         localfile = {2001 - Fleischhack - On the support of physical measures in gauge theories.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0109030\\;\%\%},
         title = {{On the support of physical measures in gauge theories}},
         url = {http://arxiv.org/abs/math-ph/0109030},
         year = {2001}
 }
 
 @article{Kunhardt:2001,
         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.},
         author = {W. Kunhardt},
         eprint = {math-ph/0109001},
         localfile = {2001 - Kunhardt - On Infravacua and the Superselection Structure of Theories with Massless Particles.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0109001\\;\%\%},
         title = {{On infravacua and the superselection structure of theories with massless particles}},
         url = {http://arxiv.org/abs/math-ph/0109001},
         year = {2001}
 }
 
 @article{Mund:2001,
         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.},
         author = {J. Mund},
         eprint = {hep-th/0101227},
         journal = {Annales Henri Poincare},
         localfile = {2001 - Mund - The Bisognano Wichmann theorem for massive theories.pdf},
         pages = {907--926},
         slaccitation = {\%\%CITATION = HEP-TH/0101227\\;\%\%},
         title = {{The Bisognano-Wichmann theorem for massive theories}},
         url = {http://arxiv.org/abs/hep-th/0101227},
         volume = {2},
         year = {2001}
 }
 
 @article{Schroer:2001-1,
         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).},
         author = {B. Schroer},
         eprint = {hep-th/0108203},
         journal = {Preprint},
         localfile = {2001 - Schroer - Lightfront Formalism versus Holography + Chiral Scanning.pdf},
         slaccitation = {\%\%CITATION = HEP-TH/0108203\\;\%\%},
         title = {{Lightfront formalism versus holography and chiral scanning}},
         url = {http://arxiv.org/abs/hep-th/0108203},
         year = {2001}
 }
 
 @article{Schroer:2003,
         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.},
         author = {B. Schroer},
         eprint = {hep-th/0106066},
         journal = {Ann. Phys.},
         localfile = {2001 - Schroer - Uniqueness of Inverse Scattering Problem in Local Quantum Physics.pdf},
         pages = {421--437},
         slaccitation = {\%\%CITATION = HEP-TH/0106066\\;\%\%},
         title = {{Uniqueness of inverse scattering problem in local quantum physics}},
         url = {http://arxiv.org/abs/hep-th/0106066},
         volume = {307},
         year = {2003}
 }
 
 @article{Strohmaier:2000,
         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.},
         author = {A. Strohmaier},
         eprint = {math-ph/0008043},
         journal = {Lett. Math. Phys.},
         localfile = {2000 - Strohmaier - On the local structure of the Klein-Gordon field on curved spacetimes.pdf},
         pages = {249--261},
         slaccitation = {\%\%CITATION = MATH-PH/0008043\\;\%\%},
         title = {{On the local structure of the Klein-Gordon field on curved spacetimes}},
         url = {http://arxiv.org/abs/math-ph/0008043},
         volume = {54},
         year = {2000}
 }
 
 @article{Thiemann:2001,
         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.},
         author = {T. Thiemann},
         eprint = {gr-qc/0110034},
         localfile = {2001 - Thiemann - Introduction to modern canonical quantum general relativity.pdf},
         slaccitation = {\%\%CITATION = GR-QC/0110034\\;\%\%},
         title = {{Introduction to modern canonical quantum general relativity}},
         url = {http://arxiv.org/abs/gr-qc/0110034},
         year = {2001}
 }
 
 @article{AshtekarLewandowskiSahlmann:2003,
         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.},
         author = {A. Ashtekar and J. Lewandowski and H. Sahlmann},
         eprint = {gr-qc/0211012},
         journal = {Class. Quant. Grav.},
         localfile = {2002 - Ashtekar, Lewandowski, Sahlmann - Polymer and Fock representations for a Scalar field.pdf},
         pages = {L11--1},
         slaccitation = {\%\%CITATION = GR-QC/0211012\\;\%\%},
         title = {{Polymer and {F}ock representations for a scalar field}},
         url = {http://arxiv.org/abs/gr-qc/0211012},
         volume = {20},
         year = {2003}
 }
 
 @article{BahnsDoplicherFredenhagenPiacitelli:2002,
         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.},
         author = {D. Bahns and S. Doplicher and K. Fredenhagen and G. Piacitelli},
         doi = {10.1016/S0370-2693(02)01563-0},
         eprint = {hep-th/0201222},
         journal = {Phys. Lett.},
         keywords = {NCQFT},
         localfile = {2002 - Bahns, Doplicher, Fredenhagen, Piacitelli - On the unitarity problem in space-time noncommutative theories.pdf},
         pages = {178--181},
         slaccitation = {\%\%CITATION = HEP-TH/0201222\\;\%\%},
         title = {{On the unitarity problem in space/time noncommutative theories}},
         url = {http://arxiv.org/abs/hep-th/0201222},
         volume = {B533},
         year = {2002}
 }
 
 @article{BuchholzMundSummers:2002,
         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.},
         author = {D. Buchholz and J. Mund and S. J. Summers},
         eprint = {hep-th/0207057},
         journal = {Class. Quant. Grav.},
         localfile = {2002 - Buchholz, Mund, Summers - Covariant and quasi-covariant quantum dynamics in Robertson-Walker space-times.pdf},
         pages = {6417--6434},
         slaccitation = {\%\%CITATION = HEP-TH/0207057\\;\%\%},
         title = {{Covariant and quasi-covariant quantum dynamics in Robertson-Walker space-times}},
         url = {http://arxiv.org/abs/hep-th/0207057},
         volume = {19},
         year = {2002}
 }
 
 @article{CastroAlvaredoFring:2003,
         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.},
         author = {O. Castro-Alvaredo and A. Fring},
         eprint = {hep-th/0205076},
         journal = {Nucl. Phys.},
         localfile = {2003 - Castro-Alvaredo, Fring - From integrability to conductance, impurity systems.pdf},
         pages = {449--490},
         slaccitation = {\%\%CITATION = HEP-TH/0205076\\;\%\%},
         title = {{From integrability to conductance, impurity systems}},
         url = {http://arxiv.org/abs/hep-th/0205076},
         volume = {B649},
         year = {2003}
 }
 
 @article{FassarellaSchroer:2002,
         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.},
         author = {L. Fassarella and B. Schroer},
         eprint = {hep-th/0112168},
         journal = {J. Phys.},
         localfile = {2002 - Fassarella, Schroer - Wigner Particle Theory and Local Quantum Physics.pdf},
         pages = {9123--9164},
         slaccitation = {\%\%CITATION = HEP-TH/0112168\\;\%\%},
         title = {{Wigner particle theory and local quantum physics}},
         url = {http://arxiv.org/abs/hep-th/0112168},
         volume = {A35},
         year = {2002}
 }
 
 @article{Fleischhack:2003,
         author = {C. Fleischhack},
         journal = {J. Geom. Phys.},
         localfile = {2003 - Fleischhack - Regular connections among generalized connections.pdf},
         pages = {469--483},
         slaccitation = {\%\%CITATION = JGPHE,47,469\\;\%\%},
         title = {{Regular connections among generalized connections}},
         volume = {47},
         year = {2003}
 }
 
 @article{Sahlmann:2002,
         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.},
         author = {H. Sahlmann},
         eprint = {gr-qc/0207111},
         localfile = {2002 - Sahlmann - Some comments on the representation theory of the algebra underlying loop quantum gravity.pdf},
         slaccitation = {\%\%CITATION = GR-QC/0207111\\;\%\%},
         title = {{Some comments on the representation theory of the algebra underlying loop quantum gravity}},
         url = {http://arxiv.org/abs/gr-qc/0207111},
         year = {2002}
 }
 
 @article{Thiemann:2003,
         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.},
         author = {T. Thiemann},
         eprint = {gr-qc/0210094},
         journal = {Lect. Notes Phys.},
         localfile = {2003 - Thiemann - Lectures on loop quantum gravity.pdf},
         pages = {41--135},
         slaccitation = {\%\%CITATION = GR-QC/0210094\\;\%\%},
         title = {{Lectures on loop quantum gravity}},
         url = {http://arxiv.org/abs/gr-qc/0210094},
         volume = {631},
         year = {2003}
 }
 
 @article{AlvarezGaumeVazquezMozo:2003,
         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.},
         author = {L. Alvarez-Gaume and M. A. Vazquez-Mozo},
         druck = {Booklet 22.07.08},
         eprint = {hep-th/0305093},
         journal = {Nucl. Phys.},
         keywords = {NCQFT},
         localfile = {2003 - Alvarez-Gaume, Vazquez-Mozo - General Properties of Noncommutative Field Theories.pdf},
         pages = {293--321},
         slaccitation = {\%\%CITATION = HEP-TH/0305093\\;\%\%},
         title = {{General properties of noncommutative field theories}},
         url = {http://arxiv.org/abs/hep-th/0305093},
         volume = {B668},
         year = {2003}
 }
 
 @article{BabujianKarowski:2004,
         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.},
         author = {H. M. Babujian and M. Karowski},
         eprint = {hep-th/0301088},
         journal = {Int. J. Mod. Phys.},
         localfile = {2003 - Babujian, Karowski - Towards the Construction of Wightman Functions of Integrable Quantum Field Theories.pdf},
         pages = {34--49},
         slaccitation = {\%\%CITATION = HEP-TH/0301088\\;\%\%},
         title = {{Towards the construction of Wightman functions of integrable quantum field theories}},
         url = {http://arxiv.org/abs/hep-th/0301088},
         volume = {A19S2},
         year = {2004}
 }
 
 @article{ChaichianNishijimaTureanu:2003,
         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.},
         author = {M. Chaichian and K. Nishijima and A. Tureanu},
         druck = {Booklet 24.07.08},
         eprint = {hep-th/0209008},
         journal = {Phys. Lett.},
         keywords = {NCQFT},
         localfile = {2003 - Chaichian, Nishijima, Tureanu - Spin-Statistics and CPT Theorems in Noncommutative Field Theory.pdf},
         pages = {146--152},
         slaccitation = {\%\%CITATION = HEP-TH/0209008\\;\%\%},
         title = {{Spin-statistics and CPT theorems in noncommutative field theory}},
         url = {http://arxiv.org/abs/hep-th/0209008},
         volume = {B568},
         year = {2003}
 }
 
 @article{Fleischhack:2003-2,
         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.},
         author = {C. Fleischhack},
         eprint = {math-ph/0304001},
         localfile = {2003 - Fleischhack - Parallel Transports in Webs.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0304001\\;\%\%},
         title = {{Parallel Transports in Webs}},
         url = {http://arxiv.org/abs/math-ph/0304001},
         year = {2003}
 }
 
 @article{Fleischhack:2004,
         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.},
         author = {C. Fleischhack},
         eprint = {math-ph/0304002},
         journal = {Commun. Math. Phys.},
         localfile = {2004 - Fleischhack - Proof of a Conjecture by Lewandowski and Thiemann.pdf},
         pages = {331--352},
         slaccitation = {\%\%CITATION = MATH-PH/0304002\\;\%\%},
         title = {{Proof of a Conjecture by Lewandowski and Thiemann}},
         url = {http://arxiv.org/abs/math-ph/0304002},
         volume = {249},
         year = {2004}
 }
 
 @article{Jkel:2004,
         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.},
         author = {C. D. J{\"{a}}kel},
         eprint = {hep-th/9803245},
         journal = {Annales Henri Poincare},
         localfile = {2004 - J\"{a}kel -%20 The Relation between KMS states for different temperatures.pdf},
         pages = {579--606},
         slaccitation = {\%\%CITATION = HEP-TH/9803245\\;\%\%},
         title = {{The relation between KMS-states for different temperatures}},
         url = {http://arxiv.org/abs/hep-th/9803245},
         volume = {5},
         year = {2004}
 }
 
 @article{RedeiSummers:2003,
         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.},
         author = {M. Redei and S. J. Summers},
         eprint = {quant-ph/0302115},
         localfile = {2003 - Redei, Summers - Remarks On Causality in Relativistic Quantum Field Theory.pdf},
         slaccitation = {\%\%CITATION = QUANT-PH/0302115\\;\%\%},
         title = {{Remarks on Causality in Relativistic Quantum Field Theory}},
         url = {http://arxiv.org/abs/quant-ph/0302115},
         year = {2003}
 }
 
 @article{Wess:2003,
         abstract = {Lecture given at BW2003 Workshop Mathematical, Theoretical and Phenomenological Challenges Beyond Standard Model\" 29 August-02 September, 2003 Vrnjacka Banja, Serbia},
         author = {J. Wess},
         eprint = {hep-th/0408080},
         localfile = {2003 - Wess - Deformed coordinate spaces: Derivatives.pdf},
         slaccitation = {\%\%CITATION = HEP-TH/0408080\\;\%\%},
         title = {{Deformed coordinate spaces: Derivatives}},
         url = {http://arxiv.org/abs/hep-th/0408080},
         year = {2003}
 }
 
 @article{Bostelmann:2005,
         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.},
         author = {H. Bostelmann},
         eprint = {math-ph/0409070},
         journal = {J. Math. Phys.},
         localfile = {2004 - Bostelmann - Phase space properties and the short distance structure in quantum field theory.pdf},
         pages = {052301},
         slaccitation = {\%\%CITATION = MATH-PH/0409070\\;\%\%},
         title = {{Phase space properties and the short distance structure in quantum field theory}},
         url = {http://arxiv.org/abs/math-ph/0409070},
         volume = {46},
         year = {2005}
 }
 
 @article{BuchholzLechner:2004,
         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.},
         author = {D. Buchholz and G. Lechner},
         doi = {10.1007/s00023-004-0190-8},
         eprint = {math-ph/0402072},
         journal = {Annales Henri Poincar\'{e}},
         localfile = {2004 - Buchholz, Lechner - Modular nuclearity and localization.pdf},
         pages = {1065--1080},
         slaccitation = {\%\%CITATION = MATH-PH/0402072\\;\%\%},
         title = {{Modular nuclearity and localization}},
         url = {http://arxiv.org/abs/math-ph/0402072},
         volume = {5},
         x-color = {#199bff},
         year = {2004}
 }
 
 @article{ChaichianMnatsakanovaNishijimaTureanuVernov:2004,
         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.},
         author = {M. Chaichian and M. N. Mnatsakanova and K. Nishijima and A. Tureanu and Y. S. Vernov},
         comments = {Only space-space NC, space and time commute},
         eprint = {hep-th/0402212},
         journal = {Preprint},
         keywords = {NCQFT},
         localfile = {2004 - Chaichian, Mnatsakanova, Nishijima, Tureanu, Vernov - Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory.pdf},
         slaccitation = {\%\%CITATION = HEP-TH/0402212\\;\%\%},
         title = {{Towards an axiomatic formulation of noncommutative quantum field theory}},
         url = {http://arxiv.org/abs/hep-th/0402212},
         volume = {arXiv: hep-th/0402212},
         year = {2004}
 }
 
 @article{Fewster:2004,
         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.},
         author = {C. J. Fewster},
         eprint = {gr-qc/0409043},
         localfile = {2004 - Fewster - Comments on 'Counter example to the quantum inequality'.pdf},
         slaccitation = {\%\%CITATION = GR-QC/0409043\\;\%\%},
         title = {{Comments on 'Counter example to the quantum inequality'}},
         url = {http://arxiv.org/abs/gr-qc/0409043},
         year = {2004}
 }
 
 @article{Fewster:2004-1,
         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.},
         author = {C. J. Fewster},
         eprint = {gr-qc/0411114},
         journal = {Phys. Rev.},
         localfile = {2004 - Fewster - Quantum energy inequalities in two dimensions.pdf},
         pages = {127501},
         slaccitation = {\%\%CITATION = GR-QC/0411114\\;\%\%},
         title = {{Quantum energy inequalities in two dimensions}},
         url = {http://arxiv.org/abs/gr-qc/0411114},
         volume = {D70},
         year = {2004}
 }
 
 @article{KawahigashiLongo:2005,
         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.},
         author = {Y. Kawahigashi and R. Longo},
         eprint = {math-ph/0405037},
         journal = {Commun. Math. Phys.},
         localfile = {2004 - Kawahigashi, Longo - Noncommutative Spectral Invariants and Black Hole Entropy.pdf},
         pages = {193--225},
         slaccitation = {\%\%CITATION = MATH-PH/0405037\\;\%\%},
         title = {{Noncommutative Spectral Invariants and Black Hole Entropy}},
         url = {http://arxiv.org/abs/math-ph/0405037},
         volume = {257},
         year = {2005}
 }
 
 @article{Lechner:2005,
         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.},
         author = {G. Lechner},
         doi = {10.1088/0305-4470},
         eprint = {math-ph/0405062},
         journal = {J. Phys.},
         localfile = {2005 - Lechner - On the existence of local observables in theories with a factorizing S-Matrix.pdf},
         pages = {3045--3056},
         slaccitation = {\%\%CITATION = MATH-PH/0405062\\;\%\%},
         title = {{On the existence of local observables in theories with a factorizing S-matrix}},
         url = {http://arxiv.org/abs/math-ph/0405062},
         volume = {A38},
         x-color = {#199bff},
         year = {2005}
 }
 
 @article{LongoRehren:2004,
         abstract = {Conformal field theory on the half-space x\&gt;0 of Minkowski space-time (boundary CFT\") is analyzed from an algebraic point of view, clarifying in particular the algebraic structure of local algebras and the bi-localized charge structure of local fields. The field content and the admissible boundary conditions are characterized in terms of a non-local chiral field algebra.},
         author = {R. Longo and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         doi = {10.1142/S0129055X04002163},
         eprint = {math-ph/0405067},
         journal = {Rev. Math. Phys.},
         localfile = {2004 - Longo, Rehren - Local fields in boundary conformal QFT.pdf},
         pages = {909},
         slaccitation = {\%\%CITATION = MATH-PH/0405067\\;\%\%},
         title = {{Local fields in boundary conformal {QFT}}},
         url = {http://arxiv.org/abs/math-ph/0405067},
         volume = {16},
         year = {2004}
 }
 
 @article{Schroer:2005,
         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.},
         author = {B. Schroer},
         eprint = {hep-th/0405105},
         journal = {Ann. Phys.},
         localfile = {2005 - Schroer - An anthology of non-local QFT and QFT on noncommutative spacetime.pdf},
         pages = {92--122},
         slaccitation = {\%\%CITATION = HEP-TH/0405105\\;\%\%},
         title = {{An anthology of non-local QFT and QFT on noncommutative spacetime}},
         url = {http://arxiv.org/abs/hep-th/0405105},
         volume = {319},
         year = {2005}
 }
 
 @article{Ullrich:2004,
         author = {P. Ullrich},
         journal = {J. Math. Phys.},
         localfile = {2004 - Ullrich - On the restriction of quantum fields to a lightlike surface.pdf},
         pages = {3109--3145},
         slaccitation = {\%\%CITATION = JMAPA,45,3109\\;\%\%},
         title = {{On the restriction of quantum fields to a lightlike surface}},
         volume = {45},
         year = {2004}
 }
 
 @article{Yngvason:2005,
         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.},
         author = {J. Yngvason},
         eprint = {math-ph/0411058},
         journal = {Rept. Math. Phys.},
         localfile = {2004 - Yngvason - The role of type III factors in quantum field theory.pdf},
         pages = {135--147},
         slaccitation = {\%\%CITATION = MATH-PH/0411058\\;\%\%},
         title = {{The role of type III factors in quantum field theory}},
         url = {http://arxiv.org/abs/math-ph/0411058},
         volume = {55},
         year = {2005}
 }
 
 @article{BahnsDoplicherFredenhagenPiacitelli:2005,
         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.},
         author = {D. Bahns and S. Doplicher and K. Fredenhagen and G. Piacitelli},
         eprint = {hep-th/0408204},
         journal = {Phys. Rev.},
         keywords = {NCQFT},
         localfile = {2005 - Bahns, Doplicher, Fredenhagen, Piacitelli - Field Theory on Noncommutative Spacetimes - Quasiplanar Wick Products.pdf},
         pages = {025022},
         slaccitation = {\%\%CITATION = HEP-TH/0408204\\;\%\%},
         title = {{Field theory on noncommutative spacetimes: Quasiplanar Wick products}},
         url = {http://arxiv.org/abs/hep-th/0408204},
         volume = {D71},
         year = {2005}
 }
 
 @article{BalachandranManganoPinzulVaidya:2006,
         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.},
         author = {A. P. Balachandran and G. Mangano and A. Pinzul and S. Vaidya},
         eprint = {hep-th/0508002},
         journal = {Int. J. Mod. Phys.},
         keywords = {NCQFT},
         localfile = {2005 - Balachandran, Mangano, Pinzul, Vaidya - Spin and Statistics on the Groenewold-Moyal Plane - Pauli-Forbidden Levels and Transitions.pdf},
         pages = {3111--3126},
         slaccitation = {\%\%CITATION = HEP-TH/0508002\\;\%\%},
         title = {{Spin and statistics on the Groenwald-Moyal plane: Pauli- forbidden levels and transitions}},
         url = {http://arxiv.org/abs/hep-th/0508002},
         volume = {A21},
         year = {2006}
 }
 
 @article{BuchholzSummers:2005,
         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.},
         author = {D. Buchholz and S. J. Summers},
         eprint = {math-ph/0509047},
         journal = {Preprint},
         localfile = {2005 - Buchholz, Summers - Scattering in Relativistic Quantum Field Theory - Fundamental Concepts and Tools.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0509047\\;\%\%},
         title = {{Scattering in relativistic quantum field theory: Fundamental concepts and tools}},
         url = {http://arxiv.org/abs/math-ph/0509047},
         year = {2005}
 }
 
 @article{FewsterHollands:2005,
         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.},
         author = {C. J. Fewster and S. Hollands},
         eprint = {math-ph/0412028},
         journal = {Rev. Math. Phys.},
         localfile = {2005 - Fewster, Hollands - Quantum energy inequalities in two-dimensional conformal field theory.pdf},
         pages = {577},
         slaccitation = {\%\%CITATION = MATH-PH/0412028\\;\%\%},
         title = {{Quantum energy inequalities in two-dimensional conformal field theory}},
         url = {http://arxiv.org/abs/math-ph/0412028},
         volume = {17},
         year = {2005}
 }
 
 @article{GrosseWulkenhaar:2005,
         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.},
         author = {H. Grosse and R. Wulkenhaar},
         eprint = {hep-th/0401128},
         journal = {Commun. Math. Phys.},
         localfile = {2005 - Grosse, Wulkenhaar - Renormalisation of phi**4 theory on noncommutative R**4 in the matrix base.pdf},
         pages = {305--374},
         slaccitation = {\%\%CITATION = HEP-TH/0401128\\;\%\%},
         title = {{Renormalisation of phi**4 theory on noncommutative R**4 in the matrix base}},
         url = {http://arxiv.org/abs/hep-th/0401128},
         volume = {256},
         year = {2005}
 }
 
 @article{Lechner:2007,
         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.},
         author = {G. Lechner},
         journal = {Prog.Math.},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2005 - Lechner - Towards the construction of quantum field theories from a factorizing S-matrix.pdf},
         pages = {175--198},
         pdf = {http://arxiv.org/pdf/hep-th/0502184},
         title = {{Towards the construction of quantum field theories from a factorizing S-matrix}},
         url = {http://arxiv.org/abs/hep-th/0502184},
         v1descr = {Mon, 21 Feb 2005 15:33:00 GMT (26kb)},
         volume = {251},
         x-color = {#199bff},
         year = {2007}
 }
 
 @article{MnatsakanovaVernov:2005,
         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.},
         author = {M. N. Mnatsakanova and Y. S. Vernov},
         eprint = {hep-th/0403033},
         journal = {Theor. Math. Phys.},
         localfile = {2005 - Mnatsakanova, Vernov - Jost-Lehmann-Dyson representation, analyticity in angle variable and upper bounds in noncommutative quantum field theory.pdf},
         pages = {324--336},
         slaccitation = {\%\%CITATION = HEP-TH/0403033\\;\%\%},
         title = {{Jost-Lehmann-Dyson representation, analyticity in angle variable and upper bounds in noncommutative quantum field theory}},
         url = {http://arxiv.org/abs/hep-th/0403033},
         volume = {142},
         year = {2005}
 }
 
 @article{MundSchroerYngvason:2006,
         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.},
         author = {J. Mund and B. Schroer and J. Yngvason},
         doi = {10.1007/s00220-006-0067-4},
         eprint = {math-ph/0511042},
         journal = {Commun. Math. Phys.},
         localfile = {2005 - Mund, Schroer, Yngvason - String-localized quantum fields and modular localization.pdf},
         pages = {621--672},
         slaccitation = {\%\%CITATION = MATH-PH/0511042\\;\%\%},
         title = {{String-localized quantum fields and modular localization}},
         url = {http://arxiv.org/abs/math-ph/0511042},
         volume = {268},
         year = {2006}
 }
 
 @article{Saffary:2005,
         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.},
         author = {T. Saffary},
         eprint = {math-ph/0512046},
         localfile = {2005 - Saffary - Modular action on the massive algebra.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0512046\\;\%\%},
         title = {{Modular action on the massive algebra}},
         url = {http://arxiv.org/abs/math-ph/0512046},
         year = {2005}
 }
 
 @article{Salvitti:2007,
         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.},
         author = {D. Salvitti},
         eprint = {hep-th/0507107},
         journal = {Commun. Math. Phys.},
         localfile = {2007 - Salvitti - Generalized particle statistics in two-dimensions: Examples from the theory of free massive Dirac field.pdf},
         pages = {473--492},
         slaccitation = {\%\%CITATION = HEP-TH/0507107\\;\%\%},
         title = {{Generalized particle statistics in two-dimensions: Examples from the theory of free massive Dirac field}},
         url = {http://arxiv.org/abs/hep-th/0507107},
         volume = {269},
         year = {2007}
 }
 
 @article{Schroer:2005-1,
         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.},
         author = {B. Schroer},
         eprint = {hep-th/0406016},
         journal = {Ann. Phys.},
         localfile = {2005 - Schroer - Constructive proposals for QFT based on the crossing property and on lightfront holography.pdf},
         pages = {48--91},
         slaccitation = {\%\%CITATION = HEP-TH/0406016\\;\%\%},
         title = {{Constructive proposals for QFT based on the crossing property and on lightfront holography}},
         url = {http://arxiv.org/abs/hep-th/0406016},
         volume = {319},
         year = {2005}
 }
 
 @article{BahnsWaldmann:2007,
         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.},
         author = {D. Bahns and S. Waldmann},
         eprint = {math/0607745},
         journal = {Rev. Math. Phys.},
         keywords = {NCQFT; kw:local-ncqft},
         localfile = {2006 - Bahns, Waldmann - Locally Noncommutative Space-Times.pdf},
         pages = {273--306},
         slaccitation = {\%\%CITATION = MATH/0607745\\;\%\%},
         title = {{Locally Noncommutative Space-Times}},
         url = {http://arxiv.org/abs/math/0607745},
         volume = {19},
         year = {2007}
 }
 
 @article{BalachandranGovindarajanManganoPinzulQureshiVaidya:2007,
         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.},
         author = {A. P. Balachandran and T. R. Govindarajan and G. Mangano and A. Pinzul and B. A. Qureshi and S. Vaidya},
         eprint = {hep-th/0608179},
         journal = {Phys. Rev.},
         keywords = {NCQFT},
         localfile = {2006 - Balachandran, Govindarajan, Mangano, Pinzul, Qureshi, Vaidya - Statistics and UV-IR Mixing with Twisted Poincare Invariance.pdf},
         pages = {045009},
         slaccitation = {\%\%CITATION = HEP-TH/0608179\\;\%\%},
         title = {{Statistics and UV-IR mixing with twisted Poincare invariance}},
         url = {http://arxiv.org/abs/hep-th/0608179},
         volume = {D75},
         year = {2007}
 }
 
 @article{BalachandranPinzulQureshiVaidya:2006,
         abstract = {Recent work indicates an approach to the formulation of diffeomorphism invariant quantum field theories (qft's) on the Groenewold-Moyal (GM) plane. In this approach to the qft's, statistics gets twisted and the S-matrix in the non-gauge qft's become independent of the noncommutativity parameter \theta^{\mu \nu}. Here we show that the noncommutative algebra has a commutative spacetime algebra as a substructure: the Poincar\'{e} and diffeomorphism groups are based on this algebra in the twisted approach. It is natural to preserve gauge symmetries as well by basing it on this algebra. Then gravity and gauge sectors are the same those for \theta^{\mu \nu}=0, but their interaction with matter fields is sensitive to \theta^{\mu \nu}. We calculate e^- + e^- -\&gt; e^- + e^- and \gamma + e^- \-\&gt; \gamma + e^- cross-sections in the tree approximation and explicitly display their dependence on \theta^{\mu \nu}. Remarkably the zero of the elastic e^- + e^-\ -\&gt; e^- + e^- cross-section at 90-degrees in the centre-of-mass system, which is due to Pauli principle, is shifted away as a function of \theta^{\mu \nu} and energy. This shows that noncommutativity modifies Pauli principle. We study this motion of zero in detail. An important final point of this paper is the following: the S-matrix involves time-ordered products of the interaction Hamiltonian densit\y H\_I, a\nd H\_I(x) \and H\_I(y) do not commute when x and y are space-like separated. As a result, the S-matrix is not Lorentz-invariant despite the preceding efforts to maintain it.},
         author = {A. P. Balachandran and A. Pinzul and B. A. Qureshi and S. Vaidya},
         eprint = {hep-th/0608138},
         keywords = {NCQFT},
         localfile = {2006 - Balachandran, Pinzul, Qureshi, Vaidya - Poincare Invariant Gauge and Gravity Theories on the Groenewold-Moyal Plane.pdf},
         slaccitation = {\%\%CITATION = HEP-TH/0608138\\;\%\%},
         title = {{Poincare invariant gauge and gravity theories on the Groenewold-Moyal plane}},
         url = {http://arxiv.org/abs/hep-th/0608138},
         year = {2006}
 }
 
 @article{BuchholzSchlemmer:2007,
         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.},
         author = {D. Buchholz and J. Schlemmer},
         eprint = {gr-qc/0608133},
         journal = {Class. Quant. Grav.},
         localfile = {2006 - Buchholz, Schlemmer - Local Temperature in Curved Spacetime.pdf},
         pages = {F25},
         slaccitation = {\%\%CITATION = GR-QC/0608133\\;\%\%},
         title = {{Local temperature in curved spacetime}},
         url = {http://arxiv.org/abs/gr-qc/0608133},
         volume = {24},
         year = {2007}
 }
 
 @article{BytskoTeschner:2006,
         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.},
         author = {A. G. Bytsko and J. Teschner},
         eprint = {hep-th/0602093},
         journal = {J. Phys.},
         localfile = {2006 - Bytsko, Teschner - Quantization of models with non-compact quantum group symmetry: Modular XXZ magnet and lattice sinh-Gordon model.pdf},
         pages = {12927--12981},
         slaccitation = {\%\%CITATION = HEP-TH/0602093\\;\%\%},
         title = {{Quantization of models with non-compact quantum group symmetry: Modular XXZ magnet and lattice sinh-Gordon model}},
         url = {http://arxiv.org/abs/hep-th/0602093},
         volume = {A39},
         year = {2006}
 }
 
 @article{FewsterPfenning:2006,
         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.},
         author = {C. J. Fewster and M. J. Pfenning},
         eprint = {math-ph/0602042},
         journal = {J. Math. Phys.},
         localfile = {2006 - Fewster, Pfenning - Quantum energy inequalities and local covariance. I: Globally hyperbolic spacetimes.pdf},
         pages = {082303},
         slaccitation = {\%\%CITATION = MATH-PH/0602042\\;\%\%},
         title = {{Quantum energy inequalities and local covariance. I: Globally hyperbolic spacetimes}},
         url = {http://arxiv.org/abs/math-ph/0602042},
         volume = {47},
         year = {2006}
 }
 
 @article{Fleischhack:2005,
         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.},
         author = {C. Fleischhack},
         eprint = {math-ph/0601005},
         localfile = {2005 - Fleischhack - Construction of generalized connections.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0601005\\;\%\%},
         title = {{Construction of generalized connections}},
         url = {http://arxiv.org/abs/math-ph/0601005},
         year = {2005}
 }
 
 @article{Fleischhack:2004-1,
         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.},
         author = {C. Fleischhack},
         eprint = {math-ph/0407006},
         localfile = {2004 - Fleischhack - Representations of the Weyl algebra in quantum geometry.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0407006\\;\%\%},
         title = {{Representations of the Weyl algebra in quantum geometry}},
         url = {http://arxiv.org/abs/math-ph/0407006},
         year = {2004}
 }
 
 @article{WreszinskiJkel:2006,
         abstract = {We consider the formal non relativistc limit (nrl) of the :\phi^4:\_{s+1} relativistic quantum field theory (rqft), where s is the space dimension. Following work of R. Jackiw, we show that, for s=2 and a given value of the ultraviolet cutoff \kappa, there are two ways to perform the nrl: i.) fixing the renormalized mass m^2 equal to the bare mass \m\_0^2; ii.) keeping the renormalized mass fixed and different from the bare mass\ m\_0^2. In the (infinite-volume) two-particle sector the scattering amplitude tends to zero as \kapp\a -\&gt; \infty in case i.) and, in case ii.), there is a bound state, indicating that the interaction potential is attractive. As a consequence, stability of matter fails for our boson system. We discuss why both alternatives do not reproduce the low-energy behaviour of the full rqft. The singular nature of the nrl is also nicely illustrated for s=1 by a rigorous stability/instability result of a different nature.},
         author = {W. F. Wreszinski and C. D. J{\"{a}}kel},
         eprint = {math-ph/0609059},
         localfile = {2006 - J\"{a}kel, Wreszinski - Stability and related properties of vacua and ground states.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0609059\\;\%\%},
         title = {{Stability and related properties of vacua and ground states}},
         url = {http://arxiv.org/abs/math-ph/0609059},
         year = {2006}
 }
 
 @article{Kulish:2006,
         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.},
         author = {P. P. Kulish},
         eprint = {hep-th/0606056},
         localfile = {2006 - Kulish - Twists of quantum groups and noncommutative field theory.pdf},
         slaccitation = {\%\%CITATION = HEP-TH/0606056\\;\%\%},
         title = {{Twists of quantum groups and noncommutative field theory}},
         url = {http://arxiv.org/abs/hep-th/0606056},
         year = {2006}
 }
 
 @article{LewandowskiOkolowSahlmannThiemann:2005,
         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.},
         author = {J. Lewandowski and A. Okolow and H. Sahlmann and T. Thiemann},
         eprint = {gr-qc/0504147},
         localfile = {2005 - Lewandowski, Okolow, Sahlmann - Uniqueness of diffeomorphism invariant states on holonomy- flux algebras.pdf},
         slaccitation = {\%\%CITATION = GR-QC/0504147\\;\%\%},
         title = {{Uniqueness of diffeomorphism invariant states on holonomy- flux algebras}},
         url = {http://arxiv.org/abs/gr-qc/0504147},
         year = {2005}
 }
 
 @article{Zahn:2006,
         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.},
         author = {J. Zahn},
         eprint = {hep-th/0603231},
         journal = {Phys. Rev.},
         localfile = {2006 - Zahn - Remarks on twisted noncommutative quantum field theory.pdf},
         pages = {105005},
         slaccitation = {\%\%CITATION = HEP-TH/0603231\\;\%\%},
         title = {{Remarks on twisted noncommutative quantum field theory}},
         url = {http://arxiv.org/abs/hep-th/0603231},
         volume = {D73},
         year = {2006}
 }
 
 @article{BergbauerKreimer:2007,
         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.},
         author = {C. Bergbauer and D. Kreimer},
         eprint = {arXiv:0704.0232 [hep-th]},
         localfile = {2007 - Bergbauer, Kreimer - New Algebraic Aspects of Perturbative and Non-Perturbative Quantum Field Theory.pdf},
         slaccitation = {\%\%CITATION = ARXIV:0704.0232\\;\%\%},
         title = {{New algebraic aspects of perturbative and non-perturbative Quantum Field Theory}},
         url = {http://arxiv.org/abs/0704.0232},
         year = {2007}
 }
 
 @article{BrunettiGuidoLongo:2002,
         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.},
         author = {R. Brunetti and D. Guido and R. Longo},
         doi = {10.1142/S0129055X02001387},
         eprint = {math-ph/0203021},
         journal = {Rev. Math. Phys.},
         localfile = {2002 - Brunetti, Guido, Longo - Modular localization and Wigner particles.pdf},
         pages = {759--786},
         slaccitation = {\%\%CITATION = MATH-PH/0203021\\;\%\%},
         title = {{Modular localization and Wigner particles}},
         url = {http://arxiv.org/abs/math-ph/0203021},
         volume = {14},
         year = {2002}
 }
 
 @article{BuchholzGrundling:2007,
         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.},
         author = {D. Buchholz and H. Grundling},
         eprint = {arXiv:0705.1988 [math.OA]},
         localfile = {2007 - Buchholz, Grundling - The resolvent algebra: A new approach to canonical quantum systems.pdf},
         slaccitation = {\%\%CITATION = ARXIV:0705.1988\\;\%\%},
         title = {{The resolvent algebra: A new approach to canonical quantum systems}},
         url = {http://arxiv.org/abs/0705.1988},
         year = {2007}
 }
 
 @article{BuchholzLongo:1999,
         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.},
         author = {D. Buchholz and R. Longo},
         eprint = {hep-th/9905102},
         journal = {Adv. Theor. Math. Phys.},
         localfile = {2000 - Buchholz, Longo - Graded KMS Functionals and the Breakdown of Supersymmetry.pdf},
         pages = {615--626},
         slaccitation = {\%\%CITATION = HEP-TH/9905102\\;\%\%},
         title = {{Graded KMS functionals and the breakdown of supersymmetry}},
         url = {http://arxiv.org/abs/hep-th/9905102},
         volume = {3},
         year = {1999}
 }
 
 @article{Fewster:2006,
         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.},
         author = {C. J. Fewster},
         eprint = {math-ph/0611058},
         localfile = {2006 - Fewster - Quantum energy inequalities and local covariance. II: Categorical formulation.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0611058\\;\%\%},
         title = {{Quantum energy inequalities and local covariance. II: Categorical formulation}},
         url = {http://arxiv.org/abs/math-ph/0611058},
         year = {2006}
 }
 
 @techreport{Fiore:2007,
         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.},
         author = {G. Fiore},
         keywords = {High Energy Physics - Theory (hep-th)},
         number = {Preprint 07-16 Dip. Matematica e Applicazioni, Universit\`{a} di Napoli; DSF/12-2007},
         pdf = {http://arxiv.org/pdf/0705.1120},
         title = {{Can QFT on Moyal-Weyl spaces look as on commutative ones?}},
         url = {http://arxiv.org/abs/0705.1120},
         v1descr = {Tue, 8 May 2007 16:11:31 GMT (11kb)},
         year = {2007}
 }
 
 @article{FioreWess:2007,
         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.},
         author = {G. Fiore and J. Wess},
         eprint = {hep-th/0701078},
         journal = {Phys. Rev.},
         keywords = {NCQFT},
         localfile = {2007 - Fiore, Wess - On full twisted Poincare' symmetry and QFT on Moyal-Weyl spaces.pdf},
         pages = {105022},
         slaccitation = {\%\%CITATION = HEP-TH/0701078\\;\%\%},
         title = {{On 'full' twisted {P}oincare' symmetry and {QFT} on {M}oyal-{W}eyl spaces}},
         url = {http://arxiv.org/abs/hep-th/0701078},
         volume = {D75},
         year = {2007}
 }
 
 @article{GuidoLongoWiesbrock:1998,
         abstract = {Starting with a conformal Quantum Field Theory on the real line, we show that the dual net is still conformal with respect to a new representation of the Moebius group. We infer from this that every conformal net is normal and conormal, namely the local von Neumann algebra associated with an interval coincides with its double relative commutant inside the local von Neumann algebra associated with any larger interval. The net and the dual net give together rise to an infinite dimensional symmetry group, of which we study a class of positive energy irreducible representations. We mention how superselsection sectors extend to the dual net and we illustrate by examples how, in general, this process generates solitonic sectors. We describe the free theories associated with the lowest weight n representations of PSL(2,R), showing that they violate 3-regularity for n\&gt;2. When \n\&gt;1, we obtain examples of non Moebius-covariant sectors of a 3-regular (non 4-regular) net.},
         author = {D. Guido and R. Longo and H.W. Wiesbrock},
         eprint = {hep-th/9703129},
         journal = {Commun. Math. Phys.},
         localfile = {1998 - Guido, Longo, Wiesbrock - Extensions of Conformal Nets and Superselection Structures.pdf},
         pages = {217--244},
         slaccitation = {\%\%CITATION = HEP-TH/9703129\\;\%\%},
         title = {{Extensions of conformal nets and superselection structures}},
         url = {http://arxiv.org/abs/hep-th/9703129},
         volume = {192},
         year = {1998}
 }
 
 @article{Hlzler:2007,
         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.},
         author = {H. H{\"{o}}lzler},
         journal = {JHEP},
         keywords = {High Energy Physics - Theory (hep-th)},
         pages = {022},
         pdf = {http://arxiv.org/pdf/0704.3392},
         title = {{World Graph Formalism for Feynman Amplitudes}},
         url = {http://arxiv.org/abs/0704.3392},
         v1descr = {Wed, 25 Apr 2007 15:14:42 GMT (58kb)},
         v1url = {http://www.arxiv.org/abs/0704.3392v1},
         v2descr = {Thu, 26 Apr 2007 08:09:05 GMT (58kb)},
         v2url = {http://www.arxiv.org/abs/0704.3392v2},
         v3descr = {Mon, 21 Apr 2008 22:28:48 GMT (62kb)},
         v3url = {http://www.arxiv.org/abs/0704.3392v3},
         v4descr = {Tue, 19 Aug 2008 20:46:22 GMT (63kb)},
         volume = {0809},
         year = {2008}
 }
 
 @phdthesis{Lechner:2006,
         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.},
         author = {G. Lechner},
         eprint = {math-ph/0611050},
         journal = {PhDThesis},
         localfile = {2006 - Lechner - On the Construction of Quantum Field Theories with Factorizing S-Matrices-PhD-Thesis.pdf},
         school = {University of G\"{o}ttingen},
         slaccitation = {\%\%CITATION = MATH-PH/0611050\\;\%\%},
         title = {{On the construction of quantum field theories with factorizing S-matrices}},
         url = {http://arxiv.org/abs/math-ph/0611050},
         x-color = {#199bff},
         year = {2006}
 }
 
 @article{Lorenzen:2007,
         author = {R. Lorenzen},
         localfile = {2007 - Lorenzen - From Spin Groups and Modular P_1CT Symmetry to Covariant Representations and the Spin-Statistics Theorem.pdf},
         note = {DESY-THESIS-2007-009},
         title = {{From spin groups and modular P(1)CT symmetry to covariant representations and the spin-statistics theorem}},
         year = {2007}
 }
 
 @article{Olbermann:2007,
         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.},
         author = {H. Olbermann},
         journal = {Class.Quant.Grav.},
         keywords = {General Relativity and Quantum Cosmology (gr-qc)},
         pages = {5011--5030},
         pdf = {http://arxiv.org/pdf/0704.2986},
         title = {{States of Low Energy on Robertson-Walker Spacetimes}},
         url = {http://arxiv.org/abs/0704.2986},
         v1descr = {Mon, 23 Apr 2007 14:53:42 GMT (22kb)},
         v1url = {http://www.arxiv.org/abs/0704.2986v1},
         v2descr = {Mon, 30 Apr 2007 14:01:09 GMT (22kb)},
         volume = {24},
         year = {2007}
 }
 
 @misc{Schlemmer:2007,
         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.},
         author = {J. Schlemmer},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2007 - Schlemmer - Local Thermal Equilibrium States and Unruh Detectors in Quantum Field Theory.pdf},
         month = feb,
         pdf = {http://arxiv.org/pdf/hep-th/0702096},
         title = {{Local Thermal Equilibrium States and Unruh Detectors in Quantum Field Theory}},
         url = {http://arxiv.org/abs/hep-th/0702096},
         v1descr = {Tue, 13 Feb 2007 10:29:55 GMT (11kb)},
         year = {2007}
 }
 
 @phdthesis{Weiner:2007,
         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.},
         author = {M. Weiner},
         keywords = {Functional Analysis (math.FA); Mathematical Physics (math-ph); Operator Algebras (math.OA)},
         pdf = {http://arxiv.org/pdf/math/0703336},
         title = {{Conformal covariance and related properties of chiral QFT}},
         url = {http://arxiv.org/abs/math/0703336},
         v1descr = {Mon, 12 Mar 2007 12:24:11 GMT (127kb)},
         year = {2007}
 }
 
 @article{CarpiWeiner:2005,
         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).},
         author = {S. Carpi and M. Weiner},
         eprint = {math/0407190},
         journal = {Commun. Math. Phys.},
         localfile = {2005 - Carpi, Weiner - On the uniqueness of diffeomorphism symmetry in conformal field theory.pdf},
         pages = {203--221},
         slaccitation = {\%\%CITATION = MATH/0407190\\;\%\%},
         title = {{On the uniqueness of diffeomorphism symmetry in conformal field theory}},
         url = {http://arxiv.org/abs/math/0407190},
         volume = {258},
         year = {2005}
 }
 
 @article{CarpiKawahigashiLongo:2007,
         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.},
         author = {S. Carpi and Y. Kawahigashi and R. Longo},
         journal = {Annales Henri Poincare},
         keywords = {Mathematical Physics (math-ph); Operator Algebras (math.OA)},
         localfile = {2007 - Carpi, Kawahigashi, Longo - Structure and Classification of Superconformal Nets.pdf},
         pages = {1069--1121},
         pdf = {http://arxiv.org/pdf/0705.3609},
         title = {{Structure and Classification of Superconformal Nets}},
         url = {http://arxiv.org/abs/0705.3609},
         v1descr = {Thu, 24 May 2007 16:15:15 GMT (45kb)},
         v1url = {http://www.arxiv.org/abs/0705.3609v1},
         v2descr = {Mon, 3 Mar 2008 18:07:21 GMT (48kb)},
         volume = {9},
         year = {2008}
 }
 
 @article{Pinamonti:2007,
         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.},
         author = {N. Pinamonti},
         eprint = {math-ph/0610070},
         journal = {Rev. Math. Phys.},
         localfile = {2007 - Pinamonti - On localization and position operators in Moebius covariant theories.pdf},
         pages = {385--404},
         slaccitation = {\%\%CITATION = MATH-PH/0610070\\;\%\%},
         title = {{On localization and position operators in Moebius covariant theories}},
         url = {http://arxiv.org/abs/math-ph/0610070},
         volume = {19},
         year = {2007}
 }
 
 @article{BalachandranPinzulQureshiVaidya:2007,
         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.},
         author = {A. P. Balachandran and A. Pinzul and B. A. Qureshi and S. Vaidya},
         journal = {Phys. Rev. D},
         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)},
         pages = {025020},
         pdf = {http://arxiv.org/pdf/0708.1379},
         title = {{S-Matrix on the Moyal Plane: Locality versus Lorentz Invariance}},
         url = {http://arxiv.org/abs/0708.1379},
         v1descr = {Fri, 10 Aug 2007 08:25:57 GMT (21kb)},
         v1url = {http://www.arxiv.org/abs/0708.1379v1},
         v2descr = {Thu, 16 Aug 2007 04:18:27 GMT (21kb)},
         volume = {77},
         year = {2008}
 }
 
 @article{KayLarkin:2007,
         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.},
         author = {Bernard S. Kay and Peter Larkin},
         journal = {Phys. Rev. D},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         pages = {121501},
         pdf = {http://arxiv.org/pdf/0708.1283},
         title = {{Pre-Holography}},
         url = {http://arxiv.org/abs/0708.1283},
         v1descr = {Thu, 9 Aug 2007 14:09:25 GMT (16kb)},
         v1url = {http://www.arxiv.org/abs/0708.1283v1},
         v2descr = {Mon, 10 Sep 2007 18:34:05 GMT (17kb)},
         v2url = {http://www.arxiv.org/abs/0708.1283v2},
         v3descr = {Fri, 16 May 2008 16:41:16 GMT (19kb)},
         volume = {77},
         year = {2008}
 }
 
 @article{BrosMoschella:2003,
         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.},
         author = {J. Bros and U. Moschella},
         eprint = {math-ph/0311052},
         localfile = {2003 - Bros, Moschella - Fourier analysis and holomorphic decomposition on the one- sheeted hyperboloid.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0311052\\;\%\%},
         title = {{Fourier analysis and holomorphic decomposition on the one- sheeted hyperboloid}},
         url = {http://arxiv.org/abs/math-ph/0311052},
         year = {2003}
 }
 
 @article{BertolaCorbettaMoschella:2006,
         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.},
         author = {M. Bertola and F. Corbetta and U. Moschella},
         eprint = {math-ph/0609080},
         localfile = {2006 - Bertola, Corbetta, Moschella - Massless scalar field in two-dimensional de Sitter universe.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0609080\\;\%\%},
         title = {{Massless scalar field in two-dimensional de Sitter universe}},
         url = {http://arxiv.org/abs/math-ph/0609080},
         year = {2006}
 }
 
 @article{BrosMoschella:1996,
         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.},
         author = {J. Bros and U. Moschella},
         eprint = {gr-qc/9511019},
         journal = {Rev. Math. Phys.},
         localfile = {1996 - Bros, Moschella - Two-point Functions and Quantum Fields in de Sitter Universe.pdf},
         pages = {327--392},
         slaccitation = {\%\%CITATION = GR-QC/9511019\\;\%\%},
         title = {{Two-point Functions and Quantum Fields in de Sitter Universe}},
         url = {http://arxiv.org/abs/gr-qc/9511019},
         volume = {8},
         year = {1996}
 }
 
 @article{GrosseLechner:2007,
         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.},
         author = {H. Grosse and G. Lechner},
         doi = {10.1088/1126-6708},
         eprint = {arXiv:0706.3992 [hep-th]},
         journal = {JHEP},
         keywords = {kw:NC-Wick; kw:warping},
         localfile = {2007 - Grosse, Lechner - Wedge-Local Quantum Fields and Noncommutative Minkowski Space.pdf},
         pages = {012},
         slaccitation = {\%\%CITATION = ARXIV:0706.3992\\;\%\%},
         title = {{Wedge-Local Quantum Fields and Noncommutative {M}inkowski Space}},
         url = {http://arxiv.org/abs/0706.3992},
         volume = {11},
         x-color = {#199bff},
         year = {2007}
 }
 
 @article{Knight:1961,
         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.},
         author = {J. M. Knight},
         doi = {10.1063/1.1703731},
         journal = {J. Math. Phys.},
         localfile = {1961 - Knight - Strict Localization in Quantum Field Theory.pdf},
         number = {4},
         pages = {459--471},
         title = {{Strict Localization in Quantum Field Theory}},
         url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMAPAQ000002000004000459000001&idtype=cvips&gifs=yes},
         volume = {2},
         year = {1961}
 }
 
 @article{ChamseddineFelderFrhlich:1993,
         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 $SU(2)_L\times SU(2)_R\times U(1)_{B-L}.$},
         author = {A. H. Chamseddine and G. Felder and J. Fr{\"{o}}hlich},
         eprint = {hep-ph/9209224},
         journal = {Nucl. Phys.},
         localfile = {1993 - Chamseddine, Felder, Frohlich - Grand unification in noncommutative geometry.pdf},
         pages = {672--700},
         slaccitation = {\%\%CITATION = HEP-PH/9209224\\;\%\%},
         title = {{Grand unification in noncommutative geometry}},
         url = {http://arxiv.org/abs/hep-ph/9209224},
         volume = {B395},
         year = {1993}
 }
 
 @article{FrhlichFuchsRunkelSchweigert:2004,
         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.},
         author = {J. Fr{\"{o}}hlich and J. Fuchs and I. Runkel and C. Schweigert},
         eprint = {math/0411507},
         localfile = {2004 - Fr\"{o}hlich, Fuchs, Runkel - Picard groups in rational conformal field theory.pdf},
         slaccitation = {\%\%CITATION = MATH/0411507\\;\%\%},
         title = {{Picard groups in rational conformal field theory}},
         url = {http://arxiv.org/abs/math/0411507},
         year = {2004}
 }
 
 @article{Mund:2003,
         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.},
         author = {J. Mund},
         eprint = {hep-th/0208195},
         journal = {J. Math. Phys.},
         localfile = {2003 - Mund - Modular localization of massive particles with any spin in.pdf},
         pages = {2037--2057},
         slaccitation = {\%\%CITATION = HEP-TH/0208195\\;\%\%},
         title = {{Modular localization of massive particles with any spin in D = 2+1}},
         url = {http://arxiv.org/abs/hep-th/0208195},
         volume = {44},
         year = {2003}
 }
 
 @article{Mund:1998,
         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.},
         author = {J. Mund},
         eprint = {hep-th/9712119},
         journal = {Lett. Math. Phys.},
         localfile = {1997 - Mund - No-Go Theorem for Free Relativistic Anyons in d=2+1.pdf},
         pages = {319--328},
         slaccitation = {\%\%CITATION = HEP-TH/9712119\\;\%\%},
         title = {{No-go theorem for *free* relativistic anyons in d = 2+1}},
         url = {http://arxiv.org/abs/hep-th/9712119},
         volume = {43},
         year = {1998}
 }
 
 @article{Mund:2005,
         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].)},
         author = {J. Mund},
         eprint = {hep-th/0502014},
         localfile = {2005 - Mund - String-localized covariant quantum fields.pdf},
         slaccitation = {\%\%CITATION = HEP-TH/0502014\\;\%\%},
         title = {{String-localized covariant quantum fields}},
         url = {http://arxiv.org/abs/hep-th/0502014},
         year = {2005}
 }
 
 @article{Wigner:1939,
         author = {E. P. Wigner},
         doi = {10.2307/1968551},
         journal = {Ann. Math.},
         localfile = {1939 - Wigner - On unitary representations of the inhomogeneous Lorentz group.pdf},
         title = {{On unitary representations of the inhomogeneous {L}orentz group}},
         volume = {40},
         year = {1939}
 }
 
 @article{BalachandranPinzulQureshi:2007,
         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.},
         author = {A. P. Balachandran and A. Pinzul and B. A. Qureshi},
         eprint = {arXiv:0708.1779 [hep-th]},
         keywords = {NCQFT},
         localfile = {2007 - Balachandran, Pinzul, Qureshi - Twisted Poincar'e Invariant Quantum Field Theories.pdf},
         slaccitation = {\%\%CITATION = ARXIV:0708.1779\\;\%\%},
         title = {{Twisted Poincar'e Invariant Quantum Field Theories}},
         url = {http://arxiv.org/abs/0708.1779},
         year = {2007}
 }
 
 @article{Steinacker:2007,
         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.},
         author = {H. Steinacker},
         journal = {JHEP},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
         pages = {049},
         pdf = {http://arxiv.org/pdf/0708.2426},
         title = {{Emergent Gravity from Noncommutative Gauge Theory}},
         url = {http://arxiv.org/abs/0708.2426},
         v1descr = {Mon, 20 Aug 2007 16:24:51 GMT (32kb)},
         v1url = {http://www.arxiv.org/abs/0708.2426v1},
         v2descr = {Tue, 13 Nov 2007 21:31:28 GMT (35kb)},
         v2url = {http://www.arxiv.org/abs/0708.2426v2},
         v3descr = {Wed, 19 Dec 2007 14:16:46 GMT (35kb)},
         volume = {0712},
         year = {2007}
 }
 
 @article{Hollands:2007,
         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.},
         author = {S. Hollands},
         journal = {Rev. Math. Phys.},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         pages = {1033--1172},
         pdf = {http://arxiv.org/pdf/0705.3340},
         title = {{Renormalized Quantum Yang-Mills Fields in Curved Spacetime}},
         url = {http://arxiv.org/abs/0705.3340},
         v1descr = {Wed, 23 May 2007 11:33:38 GMT (107kb)},
         v1url = {http://www.arxiv.org/abs/0705.3340v1},
         v2descr = {Wed, 13 Jun 2007 13:03:52 GMT (111kb)},
         v2url = {http://www.arxiv.org/abs/0705.3340v2},
         v3descr = {Thu, 28 Feb 2008 16:27:04 GMT (128kb)},
         volume = {20},
         year = {2008}
 }
 
 @article{Hollands:2007-1,
         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.},
         author = {S. Hollands},
         eprint = {gr-qc/0605072},
         journal = {Commun. Math. Phys.},
         localfile = {2007 - Hollands - The operator product expansion for perturbative quantum field theory in curved spacetime.pdf},
         pages = {1--36},
         slaccitation = {\%\%CITATION = GR-QC/0605072\\;\%\%},
         title = {{The operator product expansion for perturbative quantum field theory in curved spacetime}},
         url = {http://arxiv.org/abs/gr-qc/0605072},
         volume = {273},
         year = {2007}
 }
 
 @article{Hollands:2004,
         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.},
         author = {S. Hollands},
         eprint = {gr-qc/0212028},
         journal = {Commun. Math. Phys.},
         localfile = {2004 - Hollands - A general PCT theorem for the operator product expansion in curved spacetime.pdf},
         pages = {209--244},
         slaccitation = {\%\%CITATION = GR-QC/0212028\\;\%\%},
         title = {{A general PCT theorem for the operator product expansion in curved spacetime}},
         url = {http://arxiv.org/abs/gr-qc/0212028},
         volume = {244},
         year = {2004}
 }
 
 @article{KeylMatsuiSchlingemannWerner:2007,
         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.},
         author = {M. Keyl and T. Matsui and D. Schlingemann and R. F. Werner},
         journal = {Rev. Math. Phys.},
         keywords = {Mathematical Physics (math-ph)},
         pages = {707--724},
         pdf = {http://arxiv.org/pdf/math-ph/0703013},
         title = {{On Haag Duality for Pure States of Quantum Spin Chain}},
         url = {http://arxiv.org/abs/math-ph/0703013},
         v1descr = {Fri, 2 Mar 2007 06:32:05 GMT (17kb)},
         volume = {20},
         year = {2008}
 }
 
 @article{GerardJkel:2006,
         author = {C. Gerard and C. D. J{\"{a}}kel},
         eprint = {math-ph/0609088},
         localfile = {2006 - Gerard, J\"{a}kel - On the relativistic KMS condition for the P(phi)(2) model.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0609088\\;\%\%},
         title = {{On the relativistic KMS condition for the P(phi)(2) model}},
         year = {2006}
 }
 
 @article{GerardJkel:2005,
         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.},
         author = {C. Gerard and C. D. J{\"{a}}kel},
         eprint = {math-ph/0403048},
         journal = {Rev. Math. Phys.},
         localfile = {2005 - Gerard, J\"{a}kel - Thermal quantum fields without cut-offs in 1+1 space-time dimensions.pdf},
         pages = {113--174},
         slaccitation = {\%\%CITATION = MATH-PH/0403048\\;\%\%},
         title = {{Thermal quantum fields without cut-offs in 1+1 space-time dimensions}},
         url = {http://arxiv.org/abs/math-ph/0609088},
         volume = {17},
         year = {2005}
 }
 
 @article{GerardJkel:2003,
         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.},
         author = {C. Gerard and C. D. J{\"{a}}kel},
         eprint = {math-ph/0307053},
         localfile = {2003 - Gerard, J\"{a}kel - Thermal quantum fields with spatially cut-off interactions in 1+1 space-time dimensions.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0307053\\;\%\%},
         title = {{Thermal quantum fields with spatially cut-off interactions in 1+1 space-time dimensions}},
         url = {http://arxiv.org/abs/math-ph/0307053},
         year = {2003}
 }
 
 @article{JaffeJkel:2006,
         abstract = {We establish a useful identity for intertwining a creation or annihilation operator with the heat kernel of a self-interacting bosonic field theory.},
         author = {A. Jaffe and C. D. J{\"{a}}kel},
         eprint = {math-ph/0507047},
         journal = {Commun. Math. Phys.},
         localfile = {2006 - Jaffe, J\"{a}kel - An exchange identity for non-linear fields.pdf},
         pages = {283--289},
         slaccitation = {\%\%CITATION = MATH-PH/0507047\\;\%\%},
         title = {{An exchange identity for non-linear fields}},
         url = {http://arxiv.org/abs/math-ph/0507047},
         volume = {264},
         year = {2006}
 }
 
 @article{Abe:2007-1,
         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.},
         author = {Y. Abe},
         journal = {Phys. Rev. D},
         keywords = {High Energy Physics - Theory (hep-th)},
         number = {KEK-TH-1177},
         pages = {125009},
         pdf = {http://arxiv.org/pdf/0709.1010},
         title = {{On the Correspondence between Poincar\'{e} Symmetry of Commutative QFT and Twisted Poincar\'{e} Symmetry of Noncommutative QFT}},
         url = {http://arxiv.org/abs/0709.1010},
         v1descr = {Fri, 7 Sep 2007 07:38:53 GMT (13kb)},
         v1url = {http://www.arxiv.org/abs/0709.1010v1},
         v2descr = {Fri, 16 May 2008 06:57:30 GMT (14kb)},
         volume = {77},
         year = {2008}
 }
 
 @article{ZamolodchikovZamolodchikov:1979,
         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.},
         author = {A. B. Zamolodchikov and A. B. Zamolodchikov},
         doi = {10.1016/0003-4916(79)90391-9},
         journal = {Annals Phys.},
         localfile = {1979 - Zamolodchikov, Zamolodchikov - Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models.pdf},
         pages = {253--291},
         slaccitation = {\%\%CITATION = APNYA,120,253\\;\%\%},
         title = {{Factorized {S}-matrices in two dimensions as the exact solutions of certain relativistic quantum field models}},
         volume = {120},
         year = {1979}
 }
 
 @book{GlimmJaffe:1987,
         address = {New York},
         author = {J. Glimm and A. Jaffe},
         edition = {2},
         keywords = {kw:NC-Wick},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Glimm, Jaffe - Quantum Physics - A Functional Integral Point of View.djvu},
         note = {New York, Usa: Springer ( 1987) 535p},
         publisher = {Springer},
         title = {{Quantum Physics. A Functional Integral Point Of View}},
         year = {1987}
 }
 
 @article{Borchers:1992,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         doi = {10.1007/BF02099011},
         journal = {Commun. Math. Phys.},
         localfile = {1992 - Borchers - The CPT-theorem in two-dimensional theories of local observables.pdf},
         pages = {315--332},
         slaccitation = {\%\%CITATION = CMPHA,143,315\\;\%\%},
         title = {{The CPT theorem in two-dimensional theories of local observables}},
         volume = {143},
         year = {1992}
 }
 
 @article{KahlerWiesbrock:2001,
         author = {R. Kahler and H.W. Wiesbrock},
         journal = {J. Math. Phys.},
         pages = {74--86},
         slaccitation = {\%\%CITATION = JMAPA,42,74\\;\%\%},
         title = {{Modular theory and the reconstruction of four-dimensional quantum field theories}},
         volume = {42},
         year = {2001}
 }
 
 @article{SchroerWiesbrock:2000,
         author = {B. Schroer and H.W. Wiesbrock},
         eprint = {hep-th/9901031},
         journal = {Rev. Math. Phys.},
         pages = {461--473},
         slaccitation = {\%\%CITATION = HEP-TH/9901031\\;\%\%},
         title = {{Looking beyond the thermal horizon: Hidden symmetries in chiral models}},
         volume = {12},
         year = {2000}
 }
 
 @article{SchroerWiesbrock:2000-2,
         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.},
         author = {B. Schroer and H.W. Wiesbrock},
         eprint = {math-ph/9809003},
         journal = {Rev. Math. Phys.},
         localfile = {1998 - Schroer, Wiesbrock - Modular Theory and Geometry.pdf},
         pages = {139--158},
         slaccitation = {\%\%CITATION = MATH-PH/9809003\\;\%\%},
         title = {{Modular theory and geometry}},
         url = {http://arxiv.org/abs/math-ph/9809003},
         volume = {12},
         year = {2000}
 }
 
 @article{Wiesbrock:1997,
         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.},
         author = {H.W. Wiesbrock},
         journal = {Lett. Math. Phys.},
         localfile = {1997 - Wiesbrock - Symmetries and Modular Intersections of Von Neumann Algebras.pdf},
         pages = {203--212},
         slaccitation = {\%\%CITATION = LMPHD,39,203\\;\%\%},
         title = {{Symmetries and modular intersections of von Neumann algebras}},
         volume = {39},
         year = {1997}
 }
 
 @article{Wiesbrock:1998,
         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.},
         author = {H.W. Wiesbrock},
         journal = {Commun. Math. Phys.},
         localfile = {1998 - Wiesbrock - Modular Intersections of von Neumann Algebras in Quantum Field Theory.pdf},
         pages = {269--285},
         slaccitation = {\%\%CITATION = CMPHA,193,269\\;\%\%},
         title = {{Modular intersections of von-Neumann-algebras in quantum field theory}},
         volume = {193},
         year = {1998}
 }
 
 @article{NillWiesbrock:1995,
         author = {Florian Nill and H.W. Wiesbrock},
         eprint = {hep-th/9411084},
         journal = {Rev. Math. Phys.},
         pages = {599--630},
         slaccitation = {\%\%CITATION = HEP-TH/9411084\\;\%\%},
         title = {{A Comment on Jones inclusions with infinite index}},
         volume = {7},
         year = {1995}
 }
 
 @article{Wiesbrock:1995,
         author = {H.W. Wiesbrock},
         journal = {Rev. Math. Phys.},
         pages = {133--160},
         slaccitation = {\%\%CITATION = RMPHE,7,133\\;\%\%},
         title = {{Superselection structure of conformal field theory on the circle and localized Connes' cocycles}},
         volume = {7},
         year = {1995}
 }
 
 @article{Wiesbrock:1994,
         author = {H.W. Wiesbrock},
         journal = {Lett. Math. Phys.},
         localfile = {1994 - Wiesbrock - A note on strongly additive conformal field theory and half-sided modular conormal standard inclusions.pdf},
         pages = {303--308},
         slaccitation = {\%\%CITATION = LMPHD,31,303\\;\%\%},
         title = {{A Note on strongly additive conformal field theory and half sided modular conormal standard inclusions}},
         volume = {31},
         year = {1994}
 }
 
 @article{Wiesbrock:1993,
         author = {H.W. Wiesbrock},
         journal = {Commun. Math. Phys.},
         localfile = {1993 - Wiesbrock - Conformal quantum field theory and half-sided modular inclusions of von Neumann algebras.pdf},
         pages = {537--544},
         slaccitation = {\%\%CITATION = CMPHA,158,537\\;\%\%},
         title = {{Conformal quantum field theory and half sided modular inclusions of von Neumann algebras}},
         volume = {158},
         year = {1993}
 }
 
 @article{Wiesbrock:1992-1,
         author = {H.W. Wiesbrock},
         journal = {J. Math. Phys.},
         pages = {1837--1840},
         slaccitation = {\%\%CITATION = JMAPA,33,1837\\;\%\%},
         title = {{A Note on the construction of the C* algebra of bosonic strings}},
         volume = {33},
         year = {1992}
 }
 
 @article{Wiesbrock:1992,
         author = {H.W. Wiesbrock},
         journal = {Commun. Math. Phys.},
         pages = {17--42},
         slaccitation = {\%\%CITATION = CMPHA,145,17\\;\%\%},
         title = {{The Construction of the sh Lie algebra of closed bosonic strings}},
         volume = {145},
         year = {1992}
 }
 
 @article{Wiesbrock:1993-1,
         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,.},
         author = {H.W. Wiesbrock},
         journal = {Commun. Math. Phys.},
         localfile = {1993 - Wiesbrock - Half-sided modular inclusions of von-Neumann-algebras.pdf},
         pages = {83--92},
         slaccitation = {\%\%CITATION = CMPHA,157,83\\;\%\%},
         title = {{Half sided modular inclusions of von Neumann algebras}},
         volume = {157},
         year = {1993}
 }
 
 @article{Wiesbrock:1992-2,
         author = {H.W. Wiesbrock},
         journal = {Lett. Math. Phys.},
         localfile = {1992 - Wiesbrock - A comment on a recent work of Borchers.pdf},
         pages = {157--160},
         slaccitation = {\%\%CITATION = LMPHD,25,157\\;\%\%},
         title = {{A Comment on a recent work of Borchers}},
         volume = {25},
         year = {1992}
 }
 
 @article{Wiesbrock:1991,
         author = {H.W. Wiesbrock},
         journal = {Commun. Math. Phys.},
         pages = {369--397},
         slaccitation = {\%\%CITATION = CMPHA,136,369\\;\%\%},
         title = {{The C* algebra of bosonic strings}},
         volume = {136},
         year = {1991}
 }
 
 @article{BorchersBuchholzSchroer:2001,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and D. Buchholz and B. Schroer},
         doi = {10.1007/s002200100411},
         eprint = {hep-th/0003243},
         journal = {Commun. Math. Phys.},
         localfile = {2000 - Borchers, Buchholz, Schroer - Polarization-free generators and the S-matrix.pdf},
         pages = {125--140},
         slaccitation = {\%\%CITATION = HEP-TH/0003243\\;\%\%},
         title = {{Polarization-free generators and the {S}-matrix}},
         url = {http://arxiv.org/abs/hep-th/0003243},
         volume = {219},
         year = {2001}
 }
 
 @article{Yngvason:1970,
         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.},
         author = {J. Yngvason},
         journal = {Commun. Math. Phys.},
         localfile = {1970 - Yngvason - Zero-mass infinite spin representations of the Poincare group and quantum field theory.pdf},
         pages = {195--203},
         slaccitation = {\%\%CITATION = CMPHA,18,195\\;\%\%},
         title = {{Zero-mass infinite spin representations of the poincare group and quantum field theory}},
         url = {http://projecteuclid.org/euclid.cmp/1103842535},
         volume = {18},
         year = {1970}
 }
 
 @article{BuchholzDAntoniLongo:1990,
         author = {D. Buchholz and C. D'Antoni and R. Longo},
         journal = {Commun. Math. Phys.},
         localfile = {1990 - Buchholz, D'Antoni, Longo - Nuclear maps and modular structures. II. Applications to quantum field theory.pdf},
         pages = {115},
         slaccitation = {\%\%CITATION = CMPHA,129,115\\;\%\%},
         title = {{Nuclear Maps and Modular Structures 2: Applications to Quantum Field Theory}},
         volume = {129},
         year = {1990}
 }
 
 @article{BuchholzDAntoniLongo:1990-1,
         author = {D. Buchholz and C. D'Antoni and R. Longo},
         journal = {J. Funct. Anal.},
         localfile = {1990 - Buchholz, D'Antoni, Longo - Nuclear maps and modular structures 1 - general properties.pdf},
         pages = {233--250},
         title = {{Nuclear maps and modular structures. I. General properties.}},
         volume = {88},
         year = {1990}
 }
 
 @article{Fewster:2005,
         author = {C. J. Fewster},
         eprint = {math-ph/0502002},
         slaccitation = {\%\%CITATION = MATH-PH/0502002\\;\%\%},
         title = {{Quantum energy inequalities and stability conditions in quantum field theory}},
         year = {2005}
 }
 
 @article{BuchholzSummers:2004-1,
         author = {D. Buchholz and S. J. Summers},
         eprint = {math-ph/0309023},
         journal = {Commun. Math. Phys.},
         pages = {625--641},
         slaccitation = {\%\%CITATION = MATH-PH/0309023\\;\%\%},
         title = {{An algebraic characterization of vacuum states in Minkowski space. III: Poincare covariance}},
         volume = {246},
         year = {2004}
 }
 
 @article{BuchholzSummers:2004-2,
         author = {D. Buchholz and S. J. Summers},
         doi = {10.1063/1.1804230},
         eprint = {math-ph/0407011},
         journal = {J. Math. Phys.},
         localfile = {2004 - Buchholz, Summers - Stable quantum systems in anti-de Sitter space: Causality, independence and spectral properties.pdf},
         pages = {4810--4831},
         slaccitation = {\%\%CITATION = MATH-PH/0407011\\;\%\%},
         title = {{Stable quantum systems in anti-de Sitter space: Causality, independence and spectral properties}},
         url = {http://www.arxiv.org/abs/math-ph/0407011},
         volume = {45},
         year = {2004}
 }
 
 @inproceedings{Rivasseau:2007,
         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.},
         author = {V. Rivasseau},
         booktitle = {{S\'{e}minaire Poincar\'{e} X}},
         eprint = {arXiv:0705.0705 [hep-th]},
         localfile = {2007 - Rivasseau - Non-commutative renormalization.pdf},
         location = {Paris},
         pages = {15--95},
         slaccitation = {\%\%CITATION = ARXIV:0705.0705\\;\%\%},
         title = {{Non-commutative renormalization}},
         url = {http://arxiv.org/abs/0705.0705},
         year = {2007}
 }
 
 @article{Aks:1965,
         author = {S. {\AA}ks},
         doi = {10.1063/1.1704305},
         journal = {J. Math. Phys.},
         localfile = {1965 - Aks - Proof that Scattering Implies Production in Quantum Field Theory.pdf},
         pages = {516--532},
         title = {{Proof that scattering implies production in quantum field theory}},
         volume = {6},
         year = {1965}
 }
 
 @book{Araki:1999,
         address = {Oxford},
         author = {H. Araki},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Araki - Mathematical Theory of Quantum Fields.djvu},
         publisher = {Oxford University Press},
         series = {{Int. Series of Monographs on Physics}},
         title = {{Mathematical Theory of Quantum Fields}},
         year = {1999}
 }
 
 @article{ChaichianKulishNishijimaTureanu:2004,
         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.},
         author = {M. Chaichian and P. P. Kulish and K. Nishijima and A. Tureanu},
         eprint = {hep-th/0408069},
         journal = {Phys. Lett.},
         keywords = {NCQFT},
         localfile = {2004 - Chaichian, Kulish, Nishijima - On a Lorentz-invariant interpretation of noncommutative space-time and its implications on noncommutative QFT.pdf},
         pages = {98--102},
         slaccitation = {\%\%CITATION = HEP-TH/0408069\\;\%\%},
         title = {{On a {L}orentz-invariant interpretation of noncommutative space-time and its implications on noncommutative {QFT}}},
         url = {http://arxiv.org/abs/hep-th/0408069},
         volume = {B604},
         year = {2004}
 }
 
 @article{DouglasNekrasov:2001,
         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.},
         author = {M. R. Douglas and N. A. Nekrasov},
         eprint = {hep-th/0106048},
         journal = {Rev. Mod. Phys.},
         localfile = {2001 - Douglas, Nekrasov - Noncommutative field theory.pdf},
         pages = {977--1029},
         slaccitation = {\%\%CITATION = HEP-TH/0106048\\;\%\%},
         title = {{Noncommutative field theory}},
         url = {http://arxiv.org/abs/hep-th/0106048},
         volume = {73},
         year = {2001}
 }
 
 @article{BuchholzSummers:2007,
         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.},
         author = {D. Buchholz and S. J. Summers},
         doi = {10.1088/1751-8113},
         eprint = {math-ph/0512060},
         journal = {J. Phys.},
         localfile = {2007 - Buchholz, Summers - String- and Brane-Localized Causal Fields in a Strongly Nonlocal Model.pdf},
         pages = {2147--2163},
         slaccitation = {\%\%CITATION = MATH-PH/0512060\\;\%\%},
         title = {{String- and brane-localized fields in a strongly nonlocal model}},
         url = {http://arxiv.org/abs/math-ph/0512060},
         volume = {A40},
         year = {2007}
 }
 
 @inbook{Faddeev:1984,
         author = {L. D. Faddeev},
         editor = {S. P. Novikov},
         note = {In Novikov, S.p. ( Ed.): Mathematical Physics Reviews, Vol. 1, 107-155},
         pages = {107--155},
         series = {{Mathematical Physics Reviews}},
         title = {{Quantum completely integrable models in field theory}},
         volume = {1},
         year = {1984}
 }
 
 @article{Grosse:1979,
         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.},
         author = {H. Grosse},
         journal = {Phys. Lett. B},
         localfile = {1979 - Grosse - On the construction of m\"{o}ller operators for the nonlinear schr\"{o}dinger equation.pdf},
         pages = {267--271},
         title = {{On the Construction of {M}\"{o}ller Operators for the Nonlinear {S}chr\"{o}dinger Equation}},
         volume = {86},
         year = {1979}
 }
 
 @book{Iagolnitzer:1993,
         address = {Princeton},
         author = {D. Iagolnitzer},
         publisher = {Princeton University Press},
         title = {{Scattering in Quantum Field Theories}},
         year = {1993}
 }
 
 @article{Hepp:1965,
         author = {K. Hepp},
         booktitle = {{Brandeis University Summer Institute in Theoretical Physics: Axiomatic Field Theory}},
         doi = {10.1007/BF01646494},
         editor = {M. Chretien and S. Deser},
         journal = {Commun. Math. Phys.},
         localfile = {1965 - Hepp - On the connection between the LSZ and Wightman quantum field theory.pdf},
         pages = {95--111},
         publisher = {Gordon \& Breach},
         title = {{On the connection between {W}ightman and {LSZ} quantum field theory}},
         volume = {1},
         year = {1965}
 }
 
 @article{KuckertLorenzen:2007,
         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.},
         author = {B. Kuckert and R. Lorenzen},
         eprint = {math-ph/0512068},
         journal = {Commun. Math. Phys.},
         localfile = {2007 - Kuckert, Lorenzen - Spin, statistics, and reflections. II: Lorentz invariance.pdf},
         pages = {809--831},
         slaccitation = {\%\%CITATION = MATH-PH/0512068\\;\%\%},
         title = {{Spin, statistics, and reflections. {II}: {L}orentz invariance}},
         url = {http://arxiv.org/abs/math-ph/0512068},
         volume = {269},
         year = {2007}
 }
 
 @article{Lechner:2003,
         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.},
         author = {G. Lechner},
         doi = {10.1023/A:1025772304804},
         eprint = {hep-th/0303062},
         journal = {Lett. Math. Phys.},
         localfile = {2003 - Lechner - Polarization-Free Quantum Fields and Interaction.pdf},
         pages = {137--154},
         slaccitation = {\%\%CITATION = HEP-TH/0303062\\;\%\%},
         title = {{Polarization-free quantum fields and interaction}},
         url = {http://arxiv.org/abs/hep-th/0303062},
         volume = {64},
         x-color = {#199bff},
         year = {2003}
 }
 
 @article{Lechner:2008,
         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.},
         author = {G. Lechner},
         doi = {10.1007/s00220-007-0381-5},
         eprint = {math-ph/0601022},
         journal = {Commun. Math. Phys.},
         localfile = {2007 - Lechner - Construction of Quantum Field Theories with Factorizing S-matrices.pdf},
         pages = {821--860},
         slaccitation = {\%\%CITATION = MATH-PH/0601022\\;\%\%},
         title = {{Construction of Quantum Field Theories with Factorizing {S}-Matrices}},
         url = {http://arxiv.org/abs/math-ph/0601022},
         volume = {277},
         x-color = {#199bff},
         year = {2008}
 }
 
 @article{Schroer:1997-1,
         author = {B. Schroer},
         eprint = {hep-th/9702145},
         journal = {Nucl. Phys.},
         localfile = {1997 - Schroer - Modular Localization and the Bootstrap-Formfactor Program.pdf},
         pages = {547--568},
         slaccitation = {\%\%CITATION = HEP-TH/9702145\\;\%\%},
         title = {{Modular localization and the bootstrap-formfactor program}},
         url = {http://arxiv.org/abs/hep-th/9702145v1},
         volume = {B499},
         year = {1997}
 }
 
 @article{SeibergWitten:1999,
         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.},
         author = {N. Seiberg and E. Witten},
         eprint = {hep-th/9908142},
         journal = {JHEP},
         localfile = {1999 - Seiberg, Witten - String theory and noncommutative geometry.pdf},
         pages = {032},
         slaccitation = {\%\%CITATION = HEP-TH/9908142\\;\%\%},
         title = {{String theory and noncommutative geometry}},
         url = {http://arxiv.org/abs/hep-th/9908142},
         volume = {09},
         year = {1999}
 }
 
 @book{Smirnov:1992,
         address = {Singapore},
         author = {F. A. Smirnov},
         publisher = {World Scientific},
         title = {{Form Factors in Completely Integrable Models of Quantum Field Theory}},
         year = {1992}
 }
 
 @article{Szabo:2003,
         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.},
         author = {R. J. Szabo},
         eprint = {hep-th/0109162},
         journal = {Phys. Rept.},
         keywords = {NCQFT},
         localfile = {2003 - Szabo - Quantum field theory on noncommutative spaces.pdf},
         pages = {207--299},
         slaccitation = {\%\%CITATION = HEP-TH/0109162\\;\%\%},
         title = {{Quantum field theory on noncommutative spaces}},
         url = {http://arxiv.org/abs/hep-th/0109162},
         volume = {378},
         year = {2003}
 }
 
 @book{StreaterWightman:1964,
         address = {Reading, MA},
         author = {R. F. Streater and A. Wightman},
         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},
         publisher = {Benjamin-Cummings},
         title = {{PCT, Spin and Statistics, and All That}},
         year = {1964}
 }
 
 @article{EliezerWoodard:1989,
         author = {D. A. Eliezer and R. P. Woodard},
         journal = {Nucl. Phys.},
         pages = {389},
         slaccitation = {\%\%CITATION = NUPHA,B325,389\\;\%\%},
         title = {{The Problem of Nonlocality in String Theory}},
         volume = {B325},
         year = {1989}
 }
 
 @article{Kawahigashi:2007,
         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.},
         author = {Y. Kawahigashi},
         eprint = {arXiv:0704.0097 [math-ph]},
         localfile = {2007 - Kawahigashi - Conformal Field Theory and Operator Algebras.pdf},
         slaccitation = {\%\%CITATION = ARXIV:0704.0097\\;\%\%},
         title = {{Conformal Field Theory and Operator Algebras}},
         url = {http://arxiv.org/abs/0704.0097},
         year = {2007}
 }
 
 @article{HalvorsonMger:2006,
         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.},
         author = {H. Halvorson and M. M{\"{u}}ger},
         eprint = {math-ph/0602036},
         localfile = {2006 - Halvorson, M\"{u}ger - Algebraic Quantum Field Theory.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0602036\\;\%\%},
         title = {{Algebraic quantum field theory}},
         url = {http://arxiv.org/abs/math-ph/0602036},
         year = {2006}
 }
 
 @article{Kawahigashi:2002,
         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.},
         author = {Y. Kawahigashi},
         eprint = {math/0211141},
         localfile = {2002 - Kawahigashi - Classification of operator algebraic conformal field theories.pdf},
         slaccitation = {\%\%CITATION = MATH/0211141\\;\%\%},
         title = {{Classification of operator algebraic conformal field theories}},
         url = {http://arxiv.org/abs/math/0211141},
         year = {2002}
 }
 
 @article{Davidson:1996,
         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.},
         author = {D. R. Davidson},
         eprint = {hep-th/9412094},
         journal = {Lett. Math. Phys.},
         localfile = {1996 - Davidson - Endomorphism semigroups and lightlike translations.pdf},
         pages = {77--90},
         slaccitation = {\%\%CITATION = HEP-TH/9412094\\;\%\%},
         title = {{Endomorphism semigroups and lightlike translations}},
         url = {http://arxiv.org/abs/hep-th/9412094},
         volume = {38},
         year = {1996}
 }
 
 @article{Svegstrup:2007,
         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.},
         author = {R. D. Svegstrup},
         journal = {Preprint},
         localfile = {2007 - Svegstrup - Endomorphisms on Half-Sided Modular Inclusions.pdf},
         title = {{Endomorphisms on Half-Sided Modular Inclusions}},
         url = {http://arxiv.org/abs/math-ph/0610027},
         year = {2007}
 }
 
 @article{Wiesbrock:1993-2,
         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.},
         author = {H.W. Wiesbrock},
         journal = {Lett. Math. Phys.},
         localfile = {1993 - Wiesbrock - Symmetries and half-sided modular inclusions of von Neumann algebras.pdf},
         pages = {107--114},
         title = {{Symmetries and half-sided modular inclusions of von Neumann algebras}},
         volume = {28},
         year = {1993}
 }
 
 @article{BabujianKarowski:2002,
         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.},
         author = {H. M. Babujian and M. Karowski},
         eprint = {hep-th/0105178},
         journal = {Nucl. Phys.},
         localfile = {2001 - Babujian, Karowski - Exact form factors in integrable quantum field theories: the sine-Gordon model (II).pdf},
         pages = {407--455},
         slaccitation = {\%\%CITATION = HEP-TH/0105178\\;\%\%},
         title = {{Exact form factors in integrable quantum field theories: The sine-Gordon model. II}},
         url = {http://arxiv.org/abs/hep-th/0105178},
         volume = {B620},
         year = {2002}
 }
 
 @article{BabujianFoersterKarowski:2006,
         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.},
         author = {H. M. Babujian and Angela Foerster and M. Karowski},
         journal = {SIGMA},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2006 - Babujian, Foerster, Karowski - The Form Factor Program: a Review and New Results - the Nested SU(N) Off-Shell Bethe Ansatz.pdf},
         pages = {082},
         pdf = {http://arxiv.org/pdf/hep-th/0609130},
         title = {{The Form Factor Program: a Review and New Results - the Nested SU(N) Off-Shell Bethe Ansatz}},
         url = {http://arxiv.org/abs/hep-th/0609130},
         v1descr = {Tue, 19 Sep 2006 14:57:02 GMT (22kb)},
         v1url = {http://www.arxiv.org/abs/hep-th/0609130v1},
         v2descr = {Fri, 29 Sep 2006 09:05:21 GMT (22kb)},
         v2url = {http://www.arxiv.org/abs/hep-th/0609130v2},
         v3descr = {Thu, 16 Nov 2006 13:36:53 GMT (23kb)},
         v3url = {http://www.arxiv.org/abs/hep-th/0609130v3},
         v4descr = {Thu, 23 Nov 2006 15:02:55 GMT (24kb)},
         volume = {2},
         year = {2006}
 }
 
 @article{BahnsDoplicherFredenhagenPiacitelli:2003,
         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]},
         author = {D. Bahns and S. Doplicher and K. Fredenhagen and G. Piacitelli},
         eprint = {hep-th/0301100},
         journal = {Commun. Math. Phys.},
         keywords = {NCQFT},
         localfile = {2003 - Bahns, Doplicher, Fredenhagen, Piacitelli - Ultraviolet Finite Quantum Field Theory on Quantum Spacetime.pdf},
         pages = {221--241},
         slaccitation = {\%\%CITATION = HEP-TH/0301100\\;\%\%},
         title = {{Ultraviolet finite quantum field theory on quantum spacetime}},
         url = {http://arxiv.org/abs/hep-th/0301100},
         volume = {237},
         year = {2003}
 }
 
 @article{BalachandranMarquesQueirozTeotonioSobrinho:2007,
         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.},
         author = {A. P. Balachandran and A. M. Marques and A. R. Queiroz and P. Teotonio-Sobrinho},
         eprint = {hep-th/0608081},
         journal = {J. Phys.},
         keywords = {NCQFT},
         localfile = {2007 - Balachandran, Queiroz, Marques, Teotonio-Sobrinho - Deformed Kac-Moody and Virasoro Algebras.pdf},
         pages = {7789--7802},
         slaccitation = {\%\%CITATION = HEP-TH/0608081\\;\%\%},
         title = {{Deformed Kac-Moody and Virasoro algebras}},
         url = {http://arxiv.org/abs/hep-th/0608081},
         volume = {A40},
         year = {2007}
 }
 
 @article{BalachandranQueirozMarquesTeotonioSobrinho:2007,
         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 $\theta$.},
         author = {A. P. Balachandran and A. R. Queiroz and A. M. Marques and P. Teotonio-Sobrinho},
         comments = {Derivation of a deformed blackbody radiation spectrum in theories with ``worldsheet noncommutativity''.},
         druck = {Booklet 24.07.08},
         eprint = {arXiv:0706.0021 [hep-th]},
         keywords = {Lesen; NCQFT},
         lesen = {X},
         localfile = {2007 - Balachandran, Queiroz, Marques, Teotonio-Sobrinho - Quantum Fields with Noncommutative Target Spaces.pdf},
         slaccitation = {\%\%CITATION = ARXIV:0706.0021\\;\%\%},
         title = {{Quantum Fields with Noncommutative Target Spaces}},
         url = {http://arxiv.org/abs/0706.0021},
         year = {2007}
 }
 
 @article{BisognanoWichmann:1976,
         author = {J. J Bisognano and E. H. Wichmann},
         journal = {J. Math. Phys.},
         localfile = {1976 - Bisognano, Wichmann - On the Duality Condition for Quantum Fields.pdf},
         pages = {303--321},
         slaccitation = {\%\%CITATION = JMAPA,17,303\\;\%\%},
         title = {{On the Duality Condition for Quantum Fields}},
         volume = {17},
         year = {1976}
 }
 
 @article{BisognanoWichmann:1975,
         author = {J. J Bisognano and E. H. Wichmann},
         journal = {J. Math. Phys.},
         localfile = {1974 - Bisognano, Wichmann - On the Duality Condition for a Hermitian Quantum Field.pdf},
         pages = {985--1007},
         slaccitation = {\%\%CITATION = JMAPA,16,985\\;\%\%},
         title = {{On the Duality Condition for a Hermitian Scalar Field}},
         volume = {16},
         year = {1975}
 }
 
 @article{Arzano:2007,
         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.},
         author = {M. Arzano},
         journal = {Phys. Rev. D},
         keywords = {High Energy Physics - Theory (hep-th)},
         pages = {025013},
         pdf = {http://arxiv.org/pdf/0710.1083},
         title = {{Quantum fields, non-locality and quantum group symmetries}},
         url = {http://arxiv.org/abs/0710.1083},
         v1descr = {Fri, 5 Oct 2007 17:17:03 GMT (12kb)},
         v1url = {http://www.arxiv.org/abs/0710.1083v1},
         v2descr = {Fri, 8 Feb 2008 20:56:29 GMT (12kb)},
         volume = {77},
         year = {2008}
 }
 
 @article{Borchers:1999,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Commun. Math. Phys.},
         localfile = {1999 - Borchers - On the embedding of von Neumann subalgebras.pdf},
         pages = {69--79},
         title = {{On the embedding of von Neumann subalgebras}},
         volume = {205},
         year = {1999}
 }
 
 @article{Borchers:1997,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Lett. Math. Phys.},
         localfile = {1997 - Borchers - On the Lattice of Subalgebras Associated with the Principle of Half-sided Modular Inclusion.pdf},
         number = {4},
         pages = {371--390},
         title = {{On the Lattice of Subalgebras Associated with the Principle of Half-sided Modular Inclusion}},
         url = {http://www.springerlink.com/content/un027304k4m253q7/?p=1a14bec3579d46e3a219897d6845164b&pi=5},
         volume = {40},
         year = {1997}
 }
 
 @article{Borchers:1996,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Commun. Math. Phys.},
         localfile = {1996 - Borchers - Half-sided modular inclusion and the construction of the Poincare group.pdf},
         pages = {703--723},
         title = {{Half-sided modular inclusion and the construction of the Poincar\'{e} group}},
         url = {http://www.springerlink.com/content/pn7wp853n1666537/?p=98c19fdbd87648f79f623d3d44e9bf70&pi=8},
         volume = {179},
         year = {1996}
 }
 
 @article{ArakiZsido:2005,
         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.},
         author = {H. Araki and L. Zsido},
         journal = {Rev. Math. Phys.},
         localfile = {2005 - Araki, Zsido - Extension of the structure theorem of Borchers and its application to half-sided modular inclusions.pdf},
         pages = {491--543},
         title = {{Extension of the structure theorem of {B}orchers and its application to half-sided modular inclusions}},
         volume = {17},
         year = {2005}
 }
 
 @misc{ChenFrhlichPizzo:2007,
         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.},
         author = {T. Chen and J. Froehlich and A. Pizzo},
         keywords = {Mathematical Physics (math-ph)},
         month = jul,
         pdf = {http://arxiv.org/pdf/0709.2493},
         title = {{Infraparticle Scattering States in Non-Relativistic QED: I. The Bloch-Nordsieck Paradigm}},
         url = {http://arxiv.org/abs/0709.2493},
         v1descr = {Sun, 16 Sep 2007 13:43:38 GMT (166kb)},
         v1url = {http://www.arxiv.org/abs/0709.2493v1},
         v2descr = {Mon, 27 Jul 2009 19:27:25 GMT (165kb)},
         year = {2009}
 }
 
 @article{GabbianiFrhlich:1993,
         author = {F. Gabbiani and J. Fr{\"{o}}hlich},
         journal = {Commun. Math. Phys.},
         localfile = {1993 - Fr\"{o}hlich, Gabbiani - Operator algebras and conformal field theory.pdf},
         pages = {569--640},
         slaccitation = {\%\%CITATION = CMPHA,155,569\\;\%\%},
         title = {{Operator algebras and conformal field theory}},
         volume = {155},
         year = {1993}
 }
 
 @article{Jkel:1999,
         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.},
         author = {C. D. J{\"{a}}kel},
         journal = {J. Math. Phys.},
         localfile = {1999 - J\"{a}kel - Two algebraic properties of thermal quantum field theories.pdf},
         number = {12},
         pages = {6234--6244},
         title = {{Two algebraic properties of thermal quantum field theories}},
         volume = {40},
         year = {1999}
 }
 
 @article{Araki:1963,
         author = {H. Araki},
         journal = {J. Math. Phys.},
         localfile = {1963 - Araki - A Lattice of Von Neumann Algebras Associated with the Quantum Theory of a Free Bose Field.pdf},
         number = {11},
         pages = {1343--1362},
         title = {{A Lattice of von {N}eumann algebras Associated with the Quantum Theory of a Free {B}ose Field}},
         volume = {4},
         year = {1963}
 }
 
 @article{Licht:1963,
         author = {A. L. Licht},
         journal = {J. Math. Phys.},
         localfile = {1963 - Licht - Strict Localization.pdf},
         number = {11},
         pages = {1443--1447},
         title = {{Strict Localization}},
         volume = {4},
         year = {1963}
 }
 
 @article{Araki:1964,
         author = {H. Araki},
         journal = {J. Math. Phys.},
         localfile = {1964 - Araki - Von Neumann Algebras of Local Observables for Free Scalar Field.pdf},
         number = {1},
         pages = {1--13},
         title = {{Von {N}eumann Algebras of Local Observables for Free Scalar Field}},
         volume = {5},
         year = {1964}
 }
 
 @article{Borchers:1965,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Commun. Math. Phys.},
         localfile = {1965 - Borchers - Local rings and the connection of spin with statistics.pdf},
         pages = {281--307},
         title = {{Local Rings and the Connection of Spin with Statistics}},
         volume = {1},
         year = {1965}
 }
 
 @article{Borchers:1965-1,
         abstract = {The global structure analysis of local field operators is reinvestigated.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Commun. Math. Phys.},
         localfile = {1965 - Borchers - On the structure of the algebra of field operators. II.pdf},
         pages = {49--56},
         title = {{On the Structure of the Algebra of Field Operators II}},
         volume = {1},
         year = {1965}
 }
 
 @article{Borchers:1965-2,
         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).},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Commun. Math. Phys.},
         localfile = {1965 - Borchers - On the vacuum state in quantum field theory II.pdf},
         pages = {57--79},
         title = {{On the Vacuum State in Quantum Field Theory II}},
         volume = {1},
         year = {1965}
 }
 
 @article{BrosEpsteinGlaser:1965,
         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.},
         author = {J. Bros and H. Epstein and V. Glaser},
         journal = {Commun. Math. Phys.},
         localfile = {1965 - Bros, Epstein, Glaser - A proof of the crossing property for two-particle amplitudes in general quantum field theory.pdf},
         pages = {240--264},
         title = {{A Proof of the Crossing Property for Two-Particle-Amplitudes in General Quantum Field Theory }},
         volume = {1},
         year = {1965}
 }
 
 @article{BirkeFrhlich:2002,
         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.},
         author = {L. Birke and J. Fr{\"{o}}hlich},
         eprint = {math-ph/0204023},
         journal = {Rev. Math. Phys.},
         localfile = {2002 - Birke, Fr\"{o}hlich - KMS, etc.pdf},
         pages = {829--872},
         slaccitation = {\%\%CITATION = MATH-PH/0204023\\;\%\%},
         title = {{KMS, etc}},
         volume = {14},
         year = {2002}
 }
 
 @article{HaagSwieca:1965,
         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.},
         author = {R. Haag and J. A. Swieca},
         journal = {Commun. Math. Phys.},
         localfile = {1965 - Haag, Swieca - When does a quantum field theory describe particles.pdf},
         pages = {308--320},
         title = {{When does a Quantum Field Theory Describe Particles?}},
         volume = {1},
         year = {1965}
 }
 
 @article{Jaffe:1965,
         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.},
         author = {A. Jaffe},
         journal = {Commun. Math. Phys.},
         localfile = {1965 - Jaffe - Divergence of perturbation theory for bosons.pdf},
         pages = {127--149},
         title = {{Divergence of Perturbation Theory for Bosons}},
         volume = {1},
         year = {1965}
 }
 
 @article{Kastler:1965,
         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''.},
         author = {D. Kastler},
         journal = {Commun. Math. Phys.},
         localfile = {1965 - Kastler - The Cstar-algebras of a free Boson field. I. Discussion of the basic facts.pdf},
         pages = {14--48},
         title = {{The C*-Algebras of a Free Boson Field - I. Discussion of the Basic Facts }},
         volume = {1},
         year = {1965}
 }
 
 @article{LangerholcSchroer:1965,
         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.},
         author = {J. Langerholc and B. Schroer},
         journal = {Commun. Math. Phys.},
         localfile = {1965 - Langerholc, Schroer - On the structure of the von Neumann algebras generated by local functions of the free Bose field.pdf},
         pages = {215--239},
         title = {{On the Structure of the von Neumann Algebras Generated by Local Functions of the Free Bose Field }},
         volume = {1},
         year = {1965}
 }
 
 @article{Robinson:1965,
         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.},
         author = {D. W. Robinson},
         journal = {Commun. Math. Phys.},
         localfile = {1965 - Robinson - A theorem concerning the positive metric.pdf},
         pages = {89--94},
         title = {{A Theorem Concerning the Positive Metric}},
         volume = {1},
         year = {1965}
 }
 
 @article{Robinson:1965-1,
         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.},
         author = {D. W. Robinson},
         journal = {Commun. Math. Phys.},
         localfile = {1965 - Robinson - The ground state of the Bose gas.pdf},
         pages = {159--174},
         title = {{The Ground State of the Bose Gas}},
         volume = {1},
         year = {1965}
 }
 
 @article{Schlieder:1965,
         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.},
         author = {S. Schlieder},
         journal = {Commun. Math. Phys.},
         localfile = {1965 - Schlieder - Some remarks about the localization of states in a quantum field theory.pdf},
         pages = {265--280},
         title = {{Some Remarks about the Localization of States in a Quantum Field Theory*}},
         volume = {1},
         year = {1965}
 }
 
 @article{Borchers:1966,
         abstract = {The spectrum condition implies that energy and momentum are limits of local observables.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Commun. Math. Phys.},
         localfile = {1966 - Borchers - Energy and momentum as observables in quantum field theory.pdf},
         pages = {49--54},
         title = {{Energy and Momentum as Observables in Quantum Field Theory }},
         volume = {2},
         year = {1966}
 }
 
 @article{DellAntonioDoplicherRuelle:1966,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{G.-F.}}}}}}}}}}}}}}}}}}}}}}}}} Dell'Antonio and S. Doplicher and D. Ruelle},
         journal = {Commun. Math. Phys.},
         localfile = {1966 - Dell'Antonio, Doplicher, Ruelle - A theorem on canonical commutation and anticommutation relations.pdf},
         pages = {223--230},
         title = {{A Theorem on Canonical Commutation and Anticommutation Relations }},
         volume = {2},
         year = {1966}
 }
 
 @article{DoplicherKastlerRobinson:1966,
         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.},
         author = {S. Doplicher and D. Kastler and D. W. Robinson},
         journal = {Commun. Math. Phys.},
         localfile = {1966 - Doplicher, Kastler, Robinson - Covariance algebras in field theory and statistical mechanics.pdf},
         pages = {1--28},
         title = {{Covariance Algebras in Field Theory and Statistical Mechanics }},
         volume = {3},
         year = {1966}
 }
 
 @article{KadisonRingrose:1967,
         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},
         author = {R. V. Kadison and J. R. Ringrose},
         journal = {Commun. Math. Phys.},
         localfile = {1966 - Kadison, Ringrose - Derivations and automorphisms of operator algebras.pdf},
         pages = {32--63},
         title = {{Derivations and Automorphisms of Operator Algebras }},
         volume = {4},
         year = {1967}
 }
 
 @article{KastlerRobinsonSwieca:1966,
         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.},
         author = {D. Kastler and D. W. Robinson and J. A. Swieca},
         journal = {Commun. Math. Phys.},
         localfile = {1966 - Kastler, Robinson, Swieca - Conserved currents and associated symmetries Goldstone's theorem.pdf},
         pages = {108--120},
         title = {{Conserved Currents and Associated Symmetries; Goldstone's Theorem}},
         volume = {2},
         year = {1966}
 }
 
 @article{KupschSandhas:1966,
         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.},
         author = {J. Kupsch and W. Sandhas},
         journal = {Commun. Math. Phys.},
         localfile = {1966 - Kupsch, Sandhas - Moeller operators for scattering on singular potentials.pdf},
         pages = {147--154},
         title = {{Moller Operators for Scattering on Singular Potentials}},
         volume = {2},
         year = {1966}
 }
 
 @article{Lehmann:1966,
         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.},
         author = {H. Lehmann},
         journal = {Commun. Math. Phys.},
         localfile = {1966 - Lehmann - Analytic properties of scattering amplitudes in two variables in general quantum field theory.pdf},
         pages = {375--383},
         title = {{Analytic Properties of Scattering Amplitudes in two Variables in General Quantum Field Theory }},
         volume = {2},
         year = {1966}
 }
 
 @article{Licht:1966,
         author = {A. L. Licht},
         journal = {J. Math. Phys.},
         localfile = {1966 - Licht - Local States.pdf},
         number = {9},
         pages = {1656--1669},
         title = {{Local States}},
         volume = {7},
         year = {1966}
 }
 
 @article{SchroerStichel:1966,
         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.},
         author = {B. Schroer and P. Stichel},
         journal = {Commun. Math. Phys.},
         localfile = {1966 - Schroer, Stichel - Current commutation relations in the framework of general quantum field theory.pdf},
         pages = {258--281},
         title = {{Current Commutation Relations in the Framework of General Quantum Field Theory }},
         volume = {3},
         year = {1966}
 }
 
 @article{Streater:1966,
         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.},
         author = {R. F. Streater},
         journal = {Commun. Math. Phys.},
         localfile = {1966 - Streater - Canonical quantization.pdf},
         pages = {354--374},
         title = {{Canonical Quantization}},
         volume = {2},
         year = {1966}
 }
 
 @article{ArakiHaag:1967,
         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.},
         author = {H. Araki and R. Haag},
         journal = {Commun. Math. Phys.},
         localfile = {1967 - Araki, Haag - Collision cross sections in terms of local observables.pdf},
         pages = {77--91},
         title = {{Collision Cross Sections in Terms of Local Observables}},
         volume = {4},
         year = {1967}
 }
 
 @article{Borchers:1967,
         abstract = {The two sided ideals of the C*-algebra generated by local v. Neumann algebras are investigated.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Commun. Math. Phys.},
         localfile = {1967 - Borchers - A remark on a theorem of B. Misra.pdf},
         pages = {315--323},
         title = {{A Remark on a Theorem of B. Misra}},
         volume = {4},
         year = {1967}
 }
 
 @article{BrosEpsteinGlaser:1967,
         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],},
         author = {J. Bros and H. Epstein and V. Glaser},
         journal = {Commun. Math. Phys.},
         localfile = {1967 - Bros, Epstein, Glaser - On the connection between analyticity and Lorentz covariance of Wightman functions.pdf},
         pages = {77--100},
         title = {{On the Connection Between Analyticity and Lorentz Covariance of Wightman Functions }},
         volume = {6},
         year = {1967}
 }
 
 @article{EzawaSwieca:1967,
         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.},
         author = {H. Ezawa and J. A. Swieca},
         journal = {Commun. Math. Phys.},
         localfile = {1967 - Ezawa, Swieca - Spontaneous breakdown of symmetries and zero-mass states.pdf},
         pages = {330--336},
         title = {{Spontaneous Breakdown of Symmetries and Zero-Mass States}},
         volume = {5},
         year = {1967}
 }
 
 @article{Glimm:1967,
         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.},
         author = {J. Glimm},
         journal = {Commun. Math. Phys.},
         localfile = {1967 - Glimm - Yukawa coupling of quantum fields in two dimensions. I.pdf},
         pages = {34--86},
         title = {{Yukawa Coupling of Quantum Fields in Two Dimensions. I}},
         volume = {5},
         year = {1967}
 }
 
 @article{HaagHugenholtzWinnink:1967,
         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.},
         author = {R. Haag and N. M. Hugenholtz and M. Winnink},
         journal = {Commun. Math. Phys.},
         localfile = {1967 - Haag, Hugenholtz, Winnink - On the equilibrium states in quantum statistical mechanics.pdf},
         pages = {215--236},
         title = {{On the Equilibrium States in Quantum Statistical Mechanics }},
         volume = {5},
         year = {1967}
 }
 
 @article{Kadison:1967,
         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.},
         author = {R. V. Kadison},
         journal = {Commun. Math. Phys.},
         localfile = {1967 - Kadison - The energy momentum spectrum of quantum fields.pdf},
         pages = {258--260},
         title = {{The Energy Momentum Spectrum of Quantum Fields}},
         volume = {4},
         year = {1967}
 }
 
 @article{Borchers:1968,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Commun. Math. Phys.},
         localfile = {1968 - Borchers - On the converse of the Reeh-Schlieder theorem.pdf},
         pages = {269--273},
         title = {{On the Converse of the Reeh-Schlieder Theorem}},
         volume = {10},
         year = {1968}
 }
 
 @article{BorchersPohlmeyer:1968,
         abstract = {If for a relativistic field theory the expectation values of the commutator ...},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and K. Pohlmeyer},
         journal = {Commun. Math. Phys.},
         localfile = {1968 - Borchers, Pohlmeyer - Eine scheinbare Abschw\"{a}chung der Lokalit\"{a}tsbedingung II.pdf},
         title = {{Eine scheinbare Abschw\"{a}chung der Lokalit\"{a}tsbedingung. II }},
         volume = {8},
         year = {1968}
 }
 
 @article{ManuceauVerbeure:1968,
         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.},
         author = {J. Manuceau and A. Verbeure},
         journal = {Commun. Math. Phys.},
         localfile = {1968 - Manuceau, Verbeure - Quasi-free states of the CCR-algebra and Bogoliubov transformations.pdf},
         pages = {293--302},
         title = {{Quasi-Free States of the C.C.R. -- Algebra and Bogoliubov Transformations* }},
         volume = {9},
         year = {1968}
 }
 
 @article{Steinmann:1970,
         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.},
         author = {O. Steinmann},
         journal = {Commun. Math. Phys.},
         localfile = {1970 - Steinmann - Scattering formalism for non-localizable fields.pdf},
         pages = {179--194},
         title = {{Scattering Formalism for Non-Localizable Fields}},
         volume = {18},
         year = {1970}
 }
 
 @article{GlimmJaffe:1971,
         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.},
         author = {J. Glimm and A. Jaffe},
         journal = {Commun. Math. Phys.},
         localfile = {1971 - Glimm, Jaffe - Positivity and self adjointness of the P(phi)_2 Hamiltonian.pdf},
         pages = {253--258},
         title = {{Positivity and Self Adjointness of the P(φ)2 Hamiltonian }},
         volume = {22},
         year = {1971}
 }
 
 @article{OsterwalderSchrader:1973,
         abstract = {We establish necessary and sufficient conditions for Euclidean Green's functions to define a unique Wightman field theory.},
         author = {K. Osterwalder and R. Schrader},
         journal = {Commun. Math. Phys.},
         keywords = {kw:NC-Wick},
         localfile = {1973 - Osterwalder, Schrader - Axioms for Euclidean Green's functions.pdf},
         pages = {83--112},
         title = {{Axioms for Euclidean Green's Functions}},
         volume = {31},
         x-color = {#19ffd1},
         year = {1973}
 }
 
 @article{Woronowicz:1973,
         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.},
         author = {S. L. Woronowicz},
         journal = {Commun. Math. Phys.},
         localfile = {1973 - Woronowicz - On the Purification Map.pdf},
         pages = {55--67},
         title = {{On the Purification Map}},
         volume = {30},
         year = {1973}
 }
 
 @article{Buchholz:1974,
         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.},
         author = {D. Buchholz},
         journal = {Commun. Math. Phys.},
         localfile = {1974 - Buchholz - Threshold singularities of the S-matrix and convergence of Haag-Ruelle approximations.pdf},
         pages = {221--241},
         title = {{Threshold Singularities of the S-Matrix and Convergence of Haag-Ruelle Approximations }},
         volume = {39},
         year = {1974}
 }
 
 @article{Connes:1974,
         author = {A. Connes},
         journal = {Annales de l'Institut Fourier},
         localfile = {1974 - Connes - Caract\'{e}risation des espaces vectoriels ordonn\'{e}s sous-jacents aux alg\`{e}bres de von Neumann.pdf},
         pages = {121--155},
         title = {{Caract\'{e}risation des espaces vectoriels ordonn\'{e}s sous-jacents aux algebres de von Neumann}},
         volume = {24},
         year = {1974}
 }
 
 @article{Buchholz:1975,
         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.},
         author = {D. Buchholz},
         journal = {Commun. Math. Phys.},
         localfile = {1975 - Buchholz - Collision theory for waves in two dimensions and a characterization of models with trivial S-matrix.pdf},
         pages = {1--8},
         title = {{Collision Theory for Waves in Two Dimensions and a Characterization of Models with Trivial S-Matrix}},
         volume = {45},
         year = {1975}
 }
 
 @article{Frhlich:1975,
         author = {J. Fr{\"{o}}hlich},
         journal = {Phys. Rev. Lett.},
         localfile = {1975 - Fr\"{o}hlich - Quantized Sine-Gordon Equation with a Nonvanishing Mass Term in Two Space-Time Dimensions.pdf},
         number = {13},
         pages = {833--836},
         title = {{Quantized ``Sine-Gordon'' Equation with a Non-Vanishing Mass Term in Two Space-Time Dimensions}},
         volume = {34},
         year = {1975}
 }
 
 @article{Mandelstam:1975,
         author = {S. Mandelstam},
         journal = {Phys. Rev. D},
         localfile = {1975 - Mandelstam - Soliton operators for the quantized sine-Gordon equation.pdf},
         number = {10},
         pages = {3026--3030},
         title = {{Soliton operators for the quantized sine-Gordon equation}},
         volume = {11},
         year = {1975}
 }
 
 @article{BrosBuchholzGlaser:1976,
         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.},
         author = {J. Bros and D. Buchholz and V. Glaser},
         journal = {Commun. Math. Phys.},
         localfile = {1976 - Bros, Buchholz, Glaser - Constants of motion in local field theory (Coleman's theorem revisited).pdf},
         pages = {11--22},
         title = {{Constants of Motion in Local Field Theory (Coleman's Theorem Revisited) }},
         volume = {50},
         year = {1976}
 }
 
 @article{DimockEckmann:1976,
         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 (...)},
         author = {J. Dimock and {{{{{{{{{{{{{{{{{{{{{{{{{J.-P.}}}}}}}}}}}}}}}}}}}}}}}}} Eckmann},
         journal = {Commun. Math. Phys.},
         localfile = {1976 - Dimock, Eckmann - On the bound state in weakly coupled lambda(phi6-ph4)_2.pdf},
         pages = {41--54},
         title = {{On the Bound State in Weakly Coupled λ(φ -----------------------------------------------------------------------------φ )2 }},
         volume = {51},
         year = {1976}
 }
 
 @article{Frhlich:1976,
         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.},
         author = {J. Fr{\"{o}}hlich},
         journal = {Commun. Math. Phys.},
         localfile = {1976 - Fr\"{o}hlich - New super-selection sectors (``soliton-states'') in two dimensional Bose quantum field models.pdf},
         pages = {269--310},
         title = {{New Super-Selection Sectors (``Soliton-States'') in Two Dimensional Bose Quantum Field Models }},
         volume = {47},
         year = {1976}
 }
 
 @article{PerezWilde:1977,
         author = {J. F. Perez and I. F. Wilde},
         journal = {Phys. Rev. D},
         localfile = {1977 - Perez, Wilde - Localization and causality in relativistic quantum mechanics.pdf},
         number = {2},
         pages = {315--317},
         title = {{Localization and Causality in Relativistic Quantum Mechanics}},
         volume = {16},
         year = {1977}
 }
 
 @article{BergKarowskiWeisz:1979,
         author = {B. Berg and M. Karowski and P. Weisz},
         journal = {Phys. Rev. D},
         localfile = {1979 - Berg, Karowski, Weisz - Construction of Green's functions from an exact S matrix.pdf},
         number = {8},
         pages = {2477--2479},
         title = {{Construction of Green's Functions from an Exact S-Matrix}},
         volume = {19},
         year = {1979}
 }
 
 @article{Lcke:1979,
         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.},
         author = {W. L{\"{u}}cke},
         journal = {Commun. Math. Phys.},
         localfile = {1979 - L\"{u}cke - PCT, Spin and Statistics, and All That for Nonlocal Wightman Fields.pdf},
         pages = {77--82},
         title = {{PCT, Spin and Statistics, and All That for Nonlocal Wightman Fields }},
         volume = {65},
         year = {1979}
 }
 
 @article{BorchersGarber:1980,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and W. D. Garber},
         journal = {Commun. Math. Phys.},
         localfile = {1980 - Borchers, Garber - Local theory of solutions for the O(2k+1) sigma-model.pdf},
         pages = {77--102},
         title = {{Local Theory of Solutions for the 0(2/c + l) σ-Model}},
         volume = {72},
         year = {1980}
 }
 
 @article{BorchersGarber:1980-1,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and W. D. Garber},
         journal = {Commun. Math. Phys.},
         localfile = {1980 - Borchers, Garber - Analyticity of solutions of the O(N) nonlinear sigma-model.pdf},
         pages = {299--309},
         title = {{Analyticity of Solutions of the O(N) Nonlinear σ-Model }},
         volume = {71},
         year = {1980}
 }
 
 @article{Dimock:1980,
         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.},
         author = {J. Dimock},
         journal = {Commun. Math. Phys.},
         localfile = {1980 - Dimock - Algebras of local observables on a manifold.pdf},
         pages = {219--228},
         title = {{Algebras of Local Observables on a Manifold}},
         volume = {77},
         year = {1980}
 }
 
 @article{BuchholzFredenhagen:1982,
         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.},
         author = {D. Buchholz and K. Fredenhagen},
         journal = {Commun. Math. Phys.},
         localfile = {1982 - Buchholz, Fredenhagen - Locality and the structure of particle states.pdf},
         pages = {1},
         slaccitation = {\%\%CITATION = CMPHA,84,1\\;\%\%},
         title = {{Locality and the Structure of Particle States}},
         volume = {84},
         year = {1982}
 }
 
 @article{Borchers:1983,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Commun. Math. Phys.},
         localfile = {1983 - Borchers - C-star-algebras and automorphism groups.pdf},
         pages = {95--103},
         title = {{C*-Algebras and Automorphism Groups}},
         volume = {88},
         year = {1983}
 }
 
 @article{DriesslerSummers:1983,
         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.},
         author = {W. Driessler and S. J. Summers},
         journal = {Commun. Math. Phys.},
         localfile = {1983 - Driessler, Summers - Nonexistence of quantum fields associated with two-dimensional spacelike planes.pdf},
         pages = {221--226},
         slaccitation = {\%\%CITATION = CMPHA,89,221\\;\%\%},
         title = {{NONEXISTENCE OF QUANTUM FIELDS ASSOCIATED WITH TWO- DIMENSIONAL SPACE - LIKE PLANES}},
         volume = {89},
         year = {1983}
 }
 
 @article{DoplicherLongo:1984,
         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},
         author = {S. Doplicher and R. Longo},
         journal = {Invent. Math.},
         localfile = {1984 - Doplicher, Longo - Standard and split inclusions of von Neumann algebras.pdf},
         pages = {493--536},
         title = {{Standard and split inclusions of von Neumann algebras}},
         volume = {75},
         year = {1984}
 }
 
 @article{Longo:1984,
         author = {R. Longo},
         journal = {Invent. Math.},
         localfile = {1984 - Longo - Solution of the Factorial Stone-Weierstrass conjecture.pdf},
         pages = {145--155},
         title = {{Solution of the factorial Stone-Weierstra{\ss} conjecture. An application of the theory of standard split W*-inclusions.}},
         volume = {76},
         year = {1984}
 }
 
 @article{Woronowicz:1985,
         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},
         author = {S. L. Woronowicz},
         journal = {Lett. Math. Phys.},
         localfile = {1985 - Woronowicz - On the Existence of KMS states.pdf},
         pages = {29--31},
         title = {{On the Existence of KMS States}},
         volume = {10},
         year = {1985}
 }
 
 @article{BuchholzWichmann:1986,
         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.},
         author = {D. Buchholz and E. H. Wichmann},
         journal = {Commun. Math. Phys.},
         localfile = {1986 - Buchholz, Wichmann - Causal independence and the energy-level density of states in local quantum field theory.pdf},
         pages = {321},
         slaccitation = {\%\%CITATION = CMPHA,106,321\\;\%\%},
         title = {{CAUSAL INDEPENDENCE AND THE ENERGY LEVEL DENSITY OF STATES IN LOCAL QUANTUM FIELD THEORY}},
         volume = {106},
         year = {1986}
 }
 
 @article{DAntoniDoplicherLongoFredenhagen:1987,
         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.},
         author = {C. D'Antoni and S. Doplicher and R. Longo and K. Fredenhagen},
         journal = {Commun. Math. Phys.},
         localfile = {1987 - D'Antoni, Doplicher, Fredenhagen, Longo - Convergence of Local Charges and Continuity Properties of W-Inclusions.pdf},
         pages = {325},
         slaccitation = {\%\%CITATION = CMPHA,110,325\\;\%\%},
         title = {{Convergence of Local Charges and Continuity Properties of W* Inclusions}},
         volume = {110},
         year = {1987}
 }
 
 @article{BrosIagolnitzer:1988,
         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.},
         author = {J. Bros and D. Iagolnitzer},
         journal = {Commun. Math. Phys.},
         localfile = {1988 - Bros, Iagolnitzer - 2-particle asymptotic completeness and bound states in weakly coupled quantum field theories.pdf},
         pages = {331},
         slaccitation = {\%\%CITATION = CMPHA,119,331\\;\%\%},
         title = {{TWO PARTICLE ASYMPTOTIC COMPLETENESS AND BOUND STATES IN WEAKLY COUPLED QUANTUM FIELD THEORIES}},
         volume = {119},
         year = {1988}
 }
 
 @article{Rehren:1988,
         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''.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         journal = {Commun. Math. Phys.},
         localfile = {1988 - Rehren - Locality of conformal fields in two dimensions - exchange algebra on the light-cone.pdf},
         pages = {675},
         slaccitation = {\%\%CITATION = CMPHA,116,675\\;\%\%},
         title = {{LOCALITY OF CONFORMAL FIELDS IN TWO-DIMENSIONS: EXCHANGE ALGEBRA ON THE LIGHT CONE}},
         volume = {116},
         year = {1988}
 }
 
 @article{FredenhagenRehrenSchroer:1989,
         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.},
         author = {K. Fredenhagen and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren and B. Schroer},
         journal = {Commun. Math. Phys.},
         localfile = {1989 - Fredenhagen, Rehren, Schroer - Superselection Sectors with Braid Group Statistics and Exchange Algebras I General Theory.pdf},
         pages = {201},
         slaccitation = {\%\%CITATION = CMPHA,125,201\\;\%\%},
         title = {{Superselection Sectors with Braid Group Statistics and Exchange Algebras. 1. General Theory}},
         volume = {125},
         year = {1989}
 }
 
 @article{BorchersSen:1990,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and R. N. Sen},
         journal = {Commun. Math. Phys.},
         localfile = {1990 - Borchers, Sen - Theory of ordered spaces.pdf},
         pages = {593--611},
         title = {{Theory of Ordered Spaces}},
         volume = {132},
         year = {1990}
 }
 
 @article{Buchholz:1990,
         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.},
         author = {D. Buchholz},
         journal = {Commun. Math. Phys.},
         localfile = {1990 - Buchholz - Harmonic analysis of local operators.pdf},
         pages = {631--641},
         slaccitation = {\%\%CITATION = CMPHA,129,631\\;\%\%},
         title = {{Harmonic Analysis of Local Operators}},
         volume = {129},
         year = {1990}
 }
 
 @article{Buchholz:1990-1,
         author = {D. Buchholz},
         doi = {10.1063/1.528680},
         journal = {J. Math. Phys.},
         localfile = {1990 - Buchholz - On quantum fields that generate local algebras.pdf},
         pages = {1839--1846},
         slaccitation = {\%\%CITATION = JMAPA,31,1839\\;\%\%},
         title = {{On quantum fields that generate local algebras}},
         volume = {31},
         year = {1990}
 }
 
 @article{BabelonBernard:1992,
         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.},
         author = {O. Babelon and D. Bernard},
         eprint = {hep-th/9206003},
         journal = {Phys. Lett.},
         localfile = {1992 - Babelon, Bernard - From Form Factors to Correlation Functions - The Ising Model.pdf},
         pages = {113--120},
         slaccitation = {\%\%CITATION = HEP-TH/9206003\\;\%\%},
         title = {{From form-factors to correlation functions: The {I}sing model}},
         volume = {B288},
         year = {1992}
 }
 
 @article{DimockHurd:1993,
         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.},
         author = {J. Dimock and T. R. Hurd},
         journal = {Commun. Math. Phys.},
         localfile = {1993 - Dimock, Hurd - Construction of the two-dimensional sine-Gordon model for beta less than 8 pi.pdf},
         pages = {547--580},
         title = {{Construction of the two-dimensional sine-Gordon model for beta less than 8 pi}},
         volume = {156},
         year = {1993}
 }
 
 @article{BalogHauer:1994,
         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.},
         author = {J. Balog and T. Hauer},
         eprint = {hep-th/9406155},
         journal = {Phys. Lett.},
         localfile = {1994 - Balog, Hauer - Polynomial Form Factors in the O(3) nonlinear sigma-model.pdf},
         pages = {115--121},
         slaccitation = {\%\%CITATION = HEP-TH/9406155\\;\%\%},
         title = {{Polynomial form-factors in the O(3) nonlinear sigma model}},
         volume = {B337},
         year = {1994}
 }
 
 @article{Hegerfeldt:1994,
         author = {G. C. Hegerfeldt},
         journal = {Phys. Rev. Lett.},
         localfile = {1994 - Hegerfeldt - Causality Problems for Fermis Two Atom System.pdf},
         pages = {596--599},
         slaccitation = {\%\%CITATION = PRLTA,72,596\\;\%\%},
         title = {{Causality problems for Fermi's two atom system}},
         volume = {72},
         year = {1994}
 }
 
 @article{Maison:1968,
         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.},
         author = {D. Maison},
         journal = {Commun. Math. Phys.},
         localfile = {1968 - Maison - Eine Bemerkung zu Clustereigenschaften.pdf},
         number = {1},
         pages = {48--51},
         title = {{Eine Bemerkung zu Clustereigenschaften}},
         url = {http://projecteuclid.org/euclid.cmp/1103840982},
         volume = {10},
         year = {1968}
 }
 
 @article{Dybalski:2005,
         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.},
         author = {W. Dybalski},
         eprint = {hep-th/0412226},
         journal = {Lett. Math. Phys.},
         localfile = {2004 - Dybalski - Haag-Ruelle scattering theory in presence of massless particles.pdf},
         pages = {27--38},
         slaccitation = {\%\%CITATION = HEP-TH/0412226\\;\%\%},
         title = {{Haag-Ruelle scattering theory in presence of massless particles}},
         url = {http://arxiv.org/abs/hep-th/0412226},
         volume = {72},
         year = {2005}
 }
 
 @article{Schwinger:1958,
         author = {J. Schwinger},
         journal = {Proc. Nat. Acad. Sci.},
         localfile = {1958 - Schwinger - On the Euclidian Structure of Relativistic Field Theory.pdf},
         pages = {956--965},
         title = {{On the Euclidian Structure of Relativistic Field Theory}},
         url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=528674},
         volume = {44},
         year = {1958}
 }
 
 @article{Baumann:1975,
         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.},
         author = {K. Baumann},
         journal = {Commun. Math. Phys.},
         localfile = {1975 - Baumann - When is a field theory a generalized free field.pdf},
         number = {3},
         pages = {221--223},
         title = {{When is a field theory a generalized free field?}},
         url = {http://projecteuclid.org/euclid.cmp/1103899182},
         volume = {43},
         year = {1975}
 }
 
 @article{BuchholzVerch:1995,
         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.},
         author = {D. Buchholz and R. Verch},
         eprint = {hep-th/9501063},
         journal = {Rev. Math. Phys.},
         localfile = {1995 - Buchholz, Verch - Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory.pdf},
         pages = {1195--1240},
         slaccitation = {\%\%CITATION = HEP-TH/9501063\\;\%\%},
         title = {{Scaling algebras and renormalization group in algebraic quantum field theory}},
         url = {http://arxiv.org/abs/hep-th/9501063},
         volume = {7},
         year = {1995}
 }
 
 @article{BuchholzVerch:1998,
         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.},
         author = {D. Buchholz and R. Verch},
         eprint = {hep-th/9708095},
         journal = {Rev. Math. Phys.},
         localfile = {1997 - Buchholz, Verch - Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory. II. Instructive Examples.pdf},
         pages = {775--800},
         slaccitation = {\%\%CITATION = HEP-TH/9708095\\;\%\%},
         title = {{Scaling algebras and renormalization group in algebraic quantum field theory. II: Instructive examples}},
         url = {http://arxiv.org/abs/hep-th/9708095},
         volume = {10},
         year = {1998}
 }
 
 @article{StrelchenkoVassilevich:2007,
         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.},
         author = {A. V. Strelchenko and D. V. Vassilevich},
         eprint = {arXiv:0705.4294 [hep-th]},
         journal = {Phys. Rev.},
         localfile = {2007 - Strelchenko, Vassilevich - On space-time noncommutative theories at finite temperature.pdf},
         pages = {065014},
         slaccitation = {\%\%CITATION = ARXIV:0705.4294\\;\%\%},
         title = {{On space-time noncommutative theories at finite temperature}},
         url = {http://arxiv.org/abs/0705.4294},
         volume = {D76},
         year = {2007}
 }
 
 @article{ChaichianKulishTureanuZhangZhang:2007,
         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.},
         author = {M. Chaichian and P. P. Kulish and A. Tureanu and R. B. Zhang and X. Zhang},
         journal = {J.Math.Phys.},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); NCQFT},
         pages = {042302},
         pdf = {http://arxiv.org/pdf/0711.0371},
         title = {{Noncommutative fields and actions of twisted Poincare algebra}},
         url = {http://arxiv.org/abs/0711.0371},
         v1descr = {Fri, 2 Nov 2007 18:34:47 GMT (19kb)},
         volume = {49},
         year = {2008}
 }
 
 @article{RiccardiSzabo:2007,
         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.},
         author = {Mauro Riccardi and R. J. Szabo},
         journal = {JHEP},
         keywords = {High Energy Physics - Theory (hep-th); NCQFT},
         number = {HWM-07-42, EMPG-07-22},
         pages = {016},
         pdf = {http://arxiv.org/pdf/0711.1525},
         title = {{Duality and Braiding in Twisted Quantum Field Theory}},
         url = {http://arxiv.org/abs/0711.1525},
         v1descr = {Fri, 9 Nov 2007 19:09:24 GMT (36kb)},
         v1url = {http://www.arxiv.org/abs/0711.1525v1},
         v2descr = {Mon, 10 Dec 2007 15:46:53 GMT (36kb)},
         volume = {0801},
         year = {2008}
 }
 
 @article{Schroer:2007,
         author = {B. Schroer},
         journal = {Preprint},
         localfile = {2007 - Schroer - Localization and the interface between quantum mechanics, quantum field theory and quantum gravity.pdf},
         title = {{Localization and the interface between quantum mechanics, quantum field theory and quantum gravity}},
         url = {http://www.lqp.uni-goettingen.de/papers/07/11/07111201.html},
         year = {2007}
 }
 
 @article{Schroer:2007-2,
         author = {B. Schroer},
         journal = {Preprint},
         localfile = {2007 - Schroer - Constructive use of holographic projections.pdf},
         title = {{Constructive use of holographic projections}},
         url = {http://www.lqp.uni-goettingen.de/papers/07/11/07111200.html},
         year = {2007}
 }
 
 @article{Mger:1998,
         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.},
         author = {M. M{\"{u}}ger},
         eprint = {hep-th/9705019},
         journal = {Rev. Math. Phys.},
         localfile = {1997 - M\"{u}ger - Superselection structure in massive quantum field theories in 1+1 dimensions.pdf},
         pages = {1147--1170},
         slaccitation = {\%\%CITATION = HEP-TH/9705019\\;\%\%},
         title = {{Superselection structure of massive quantum field theories in 1+1 dimensions}},
         url = {http://arxiv.org/abs/hep-th/9705019},
         volume = {10},
         year = {1998}
 }
 
 @book{Schmdgen:1990,
         address = {Basel, Boston, Berlin},
         author = {K. Schm{\"{u}}dgen},
         publisher = {Birkh\"{a}user},
         title = {{Unbounded Operator Algebras and Representation Theory}},
         year = {1990}
 }
 
 @article{BostelmannDAntoniMorsella:2007,
         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.},
         author = {H. Bostelmann and C. D'Antoni and G. Morsella},
         journal = {Commun. Math. Phys.},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Operator Algebras (math.OA)},
         number = {ESI-1985},
         pages = {763--798},
         pdf = {http://arxiv.org/pdf/0711.4237},
         title = {{Scaling algebras and pointlike fields: A nonperturbative approach to renormalization}},
         url = {http://arxiv.org/abs/0711.4237},
         v1descr = {Tue, 27 Nov 2007 12:10:48 GMT (44kb)},
         v1url = {http://www.arxiv.org/abs/0711.4237v1},
         v2descr = {Tue, 14 Oct 2008 09:58:40 GMT (45kb)},
         volume = {285},
         year = {2009}
 }
 
 @article{Abe:2007,
         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.},
         author = {Y. Abe},
         eprint = {hep-th/0606183},
         journal = {Int.J.Mod.Phys.A},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2007 - Abe - Noncommutative quantization for noncommutative field theory.pdf},
         number = {KEK-TH-1092},
         pages = {1181--1200},
         pdf = {http://arxiv.org/pdf/hep-th/0606183},
         slaccitation = {\%\%CITATION = HEP-TH/0606183\\;\%\%},
         title = {{Noncommutative Quantization for Noncommutative Field Theory}},
         url = {http://arxiv.org/abs/hep-th/0606183},
         v1descr = {Tue, 20 Jun 2006 02:26:47 GMT (22kb)},
         v1url = {http://www.arxiv.org/abs/hep-th/0606183v1},
         v2descr = {Wed, 5 Jul 2006 07:45:18 GMT (20kb)},
         v2url = {http://www.arxiv.org/abs/hep-th/0606183v2},
         v3descr = {Thu, 6 Jul 2006 13:00:26 GMT (20kb)},
         volume = {22},
         year = {2007}
 }
 
 @article{DaszkiewiczLukierskiWoronowicz:2007,
         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.},
         author = {M. Daszkiewicz and J. Lukierski and M. Woronowicz},
         journal = {Phys. Rev. D},
         keywords = {High Energy Physics - Theory (hep-th)},
         pages = {105007},
         pdf = {http://arxiv.org/pdf/0708.1561},
         title = {{Towards Quantum Noncommutative $\kappa$-deformed Field Theory}},
         url = {http://arxiv.org/abs/0708.1561},
         v1descr = {Sat, 11 Aug 2007 11:47:22 GMT (14kb)},
         v1url = {http://www.arxiv.org/abs/0708.1561v1},
         v2descr = {Thu, 27 Sep 2007 14:27:14 GMT (15kb)},
         v2url = {http://www.arxiv.org/abs/0708.1561v2},
         v3descr = {Wed, 26 Mar 2008 18:57:44 GMT (16kb)},
         volume = {77},
         year = {2008}
 }
 
 @article{GrosseWohlgenannt:2006,
         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.},
         author = {H. Grosse and M. Wohlgenannt},
         eprint = {hep-th/0507030},
         journal = {Nucl. Phys.},
         localfile = {2006 - Grosse, Wohlgenannt - On kappa-deformation and UV-IR-mixing.pdf},
         pages = {473--484},
         slaccitation = {\%\%CITATION = HEP-TH/0507030\\;\%\%},
         title = {{On kappa-deformation and UV/IR mixing}},
         url = {http://arxiv.org/abs/hep-th/0507030},
         volume = {B748},
         year = {2006}
 }
 
 @article{FreidelKowalskiGlikmanNowak:2007-1,
         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.},
         author = {L. Freidel and J. Kowalski-Glikman and S. Nowak},
         eprint = {hep-th/0612170},
         journal = {Phys. Lett.},
         localfile = {2007 - Freidel, Kowalski-Glikman, Nowak - From noncommutative kappa-Minkowski to Minkowski space- time.pdf},
         pages = {70--75},
         slaccitation = {\%\%CITATION = HEP-TH/0612170\\;\%\%},
         title = {{From noncommutative kappa-Minkowski to Minkowski space- time}},
         url = {http://arxiv.org/abs/hep-th/0612170},
         volume = {B648},
         year = {2007}
 }
 
 @article{FreidelKowalskiGlikmanNowak:2007,
         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.},
         author = {L. Freidel and J. Kowalski-Glikman and S. Nowak},
         journal = {Int.J.Mod.Phys.A},
         keywords = {High Energy Physics - Theory (hep-th)},
         pages = {2687--2718},
         pdf = {http://arxiv.org/pdf/0706.3658},
         title = {{Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry}},
         url = {http://arxiv.org/abs/0706.3658},
         v1descr = {Mon, 25 Jun 2007 14:39:17 GMT (119kb,D)},
         v1url = {http://www.arxiv.org/abs/0706.3658v1},
         v2descr = {Thu, 26 Jul 2007 09:46:25 GMT (119kb,D)},
         volume = {23},
         year = {2008}
 }
 
 @phdthesis{Bahns:2003,
         author = {D. Bahns},
         keywords = {NCQFT},
         localfile = {2003 - Bahns - Perturbative Methods on the Noncommutative Minkowski space.pdf},
         school = {University of Hamburg},
         title = {{Perturbative Methods on the Noncommutative Minkowski Space}},
         url = {http://www-library.desy.de/cgi-bin/showprep.pl?thesis04-004},
         year = {2003}
 }
 
 @article{ChaichianMnatsakanovaTureanuVernov:2006,
         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.},
         author = {M. Chaichian and M. N. Mnatsakanova and A. Tureanu and Yu. Vernov},
         eprint = {hep-th/0612112},
         keywords = {NCQFT},
         localfile = {2006 - Chaichian, Mnatsakanova, Tureanu, Vernov - Classical Theorems in Noncommutative Quantum Field Theory.pdf},
         slaccitation = {\%\%CITATION = HEP-TH/0612112\\;\%\%},
         title = {{Classical theorems in noncommutative quantum field theory}},
         url = {http://arxiv.org/abs/hep-th/0612112},
         year = {2006}
 }
 
 @article{ChaichianMnatsakanovaTureanuVernov:2006-1,
         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.},
         author = {M. Chaichian and M. N. Mnatsakanova and A. Tureanu and Yu. Vernov},
         eprint = {hep-th/0611097},
         keywords = {NCQFT},
         localfile = {2006 - Chaichian, Mnatsakanova, Tureanu - Generalized Haag's theorem in SO(1,1) and SO(1,3) invariant quantum field theory.pdf},
         slaccitation = {\%\%CITATION = HEP-TH/0611097\\;\%\%},
         title = {{Generalized Haag's theorem in SO(1,1) and SO(1,3) invariant quantum field theory}},
         url = {http://arxiv.org/abs/hep-th/0611097},
         year = {2006}
 }
 
 @article{BalachandranPinzulQureshiVaidya:2007-1,
         author = {A. P. Balachandran and A. Pinzul and B. A. Qureshi and S. Vaidya},
         eprint = {arXiv:0708.0069 [hep-th]},
         journal = {Phys. Rev.},
         keywords = {NCQFT},
         localfile = {2007 - Balachandran, Pinzul, Qureshi - Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane.pdf},
         pages = {105025},
         slaccitation = {\%\%CITATION = ARXIV:0708.0069\\;\%\%},
         title = {{Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane}},
         url = {http://arxiv.org/abs/0708.0069},
         volume = {D76},
         year = {2007}
 }
 
 @article{BuchholzOjimaRoos:2002,
         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''.},
         author = {D. Buchholz and I. Ojima and H. Roos},
         eprint = {hep-ph/0105051},
         journal = {Annals Phys.},
         localfile = {2002 - Buchholz, Ojima, Roos - Thermodynamic properties of non-equilibrium states in quantum field theory.pdf},
         pages = {219--242},
         slaccitation = {\%\%CITATION = HEP-PH/0105051\\;\%\%},
         title = {{Thermodynamic properties of non-equilibrium states in quantum field theory}},
         url = {http://arxiv.org/abs/hep-ph/0105051},
         volume = {297},
         year = {2002}
 }
 
 @article{Buchholz:2003,
         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.},
         author = {D. Buchholz},
         eprint = {hep-th/0301115},
         journal = {Commun. Math. Phys.},
         localfile = {2003 - Buchholz - On hot bangs and the arrow of time in relativistic quantum field theory.pdf},
         pages = {271--288},
         slaccitation = {\%\%CITATION = HEP-TH/0301115\\;\%\%},
         title = {{On hot bangs and the arrow of time in relativistic quantum field theory}},
         url = {http://arxiv.org/abs/hep-th/0301115},
         volume = {237},
         year = {2003}
 }
 
 @article{Camassa:2006,
         abstract = {We consider a natural generalization of Haag duality to the case in which the observable algebra is restricted to a subset of the space-time and is not irreducible: the commutant and the causal complement have to be considered relatively to the ambient space. We prove this relative form of Haag duality under quite general conditions for the free scalar and electromagnetic field of space dimension d\&gt;1 in the vacuum representation. Such property is interesting in view of a theory of superselection sectors for the electromagnetic field.},
         author = {P. Camassa},
         eprint = {math-ph/0607057},
         localfile = {2006 - Camassa - Relative Haag duality for the free field in Fock representation.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0607057\\;\%\%},
         title = {{Relative Haag duality for the free field in Fock representation}},
         url = {http://arxiv.org/abs/math-ph/0607057},
         year = {2006}
 }
 
 @article{LongoRehren:2007,
         abstract = {The relation between two-dimensional conformal quantum field theories with and without a timelike boundary is explored.},
         author = {R. Longo and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         journal = {Commun. Math. Phys.},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Operator Algebras (math.OA)},
         localfile = {2007 - Longo, Rehren - How to remove the boundary.pdf},
         pages = {1165--1182},
         pdf = {http://arxiv.org/pdf/0712.2140},
         title = {{How to remove the boundary in CFT - an operator algebraic procedure}},
         url = {http://arxiv.org/abs/0712.2140},
         v1descr = {Thu, 13 Dec 2007 12:44:57 GMT (27kb)},
         v1url = {http://www.arxiv.org/abs/0712.2140v1},
         v2descr = {Tue, 15 Jan 2008 15:39:11 GMT (27kb)},
         volume = {285},
         year = {2009}
 }
 
 @article{Seiler:2003,
         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.},
         author = {E. Seiler},
         eprint = {hep-th/0312015},
         localfile = {2003 - Seiler - The case against asymptotic freedom.pdf},
         slaccitation = {\%\%CITATION = HEP-TH/0312015\\;\%\%},
         title = {{The case against asymptotic freedom}},
         url = {http://arxiv.org/abs/hep-th/0312015},
         year = {2003}
 }
 
 @misc{Schroer:2007-1,
         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.},
         author = {B. Schroer},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2007 - Schroer - Localization-Entropy from Holography on Null-Surfaces and the Split Property.pdf},
         month = dec,
         pdf = {http://arxiv.org/pdf/0712.4403},
         title = {{Localization-Entropy from Holography on Null-Surfaces and the Split Property}},
         url = {http://arxiv.org/abs/0712.4403},
         v1descr = {Fri, 28 Dec 2007 20:36:11 GMT (35kb)},
         v1url = {http://www.arxiv.org/abs/0712.4403v1},
         v2descr = {Mon, 31 Dec 2007 18:06:18 GMT (37kb)},
         year = {2007}
 }
 
 @misc{FrhlichGawedzki:1993,
         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},
         author = {J. Fr{\"{o}}hlich and K. Gawedzki},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {1993 - Fr\"{o}hlich, Gawedzki - Conformal Field Theory and Geometry of Strings.pdf},
         month = oct,
         pdf = {http://arxiv.org/pdf/hep-th/9310187},
         title = {{Conformal Field Theory and Geometry of Strings}},
         url = {http://arxiv.org/abs/hep-th/9310187},
         v1descr = {Thu, 28 Oct 1993 21:16:54 GMT (not stored)},
         v2descr = {Sun, 31 Oct 1993 14:46:28 GMT (46kb)},
         year = {1993}
 }
 
 @article{DAntoniHollands:2006,
         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.},
         author = {C. D'Antoni and S. Hollands},
         eprint = {math-ph/0106028},
         journal = {Commun. Math. Phys.},
         localfile = {2006 - D'Antoni, Hollands - Nuclearity, local quasiequivalence and split property for Dirac quantum fields in curved spacetime.pdf},
         pages = {133--159},
         slaccitation = {\%\%CITATION = MATH-PH/0106028\\;\%\%},
         title = {{Nuclearity, local quasiequivalence and split property for Dirac quantum fields in curved spacetime}},
         url = {http://arxiv.org/abs/math-ph/0106028},
         volume = {261},
         year = {2006}
 }
 
 @article{DAntoniLongoRadulescu:2001,
         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.},
         author = {C. D'Antoni and R. Longo and F. Radulescu},
         eprint = {math/9810003},
         journal = {J. Operator Theory},
         localfile = {1998 - D'Antoni, Longo, Radulescu - Conformal Nets, Maximal Temperature and Models from Free Probability.pdf},
         pages = {195--2008},
         slaccitation = {\%\%CITATION = MATH/9810003\\;\%\%},
         title = {{Conformal Nets, Maximal Temperature and Models from Free Probability}},
         url = {http://arxiv.org/abs/math/9810003},
         volume = {45},
         year = {2001}
 }
 
 @book{Duren:1970,
         address = {New York},
         author = {P.L. Duren},
         localfile = {http://spaces.djvu},
         publisher = {Dover Publications, Inc.},
         series = {{Dover Books on Mathematics}},
         title = {{Theory of $H^p$ Spaces}},
         year = {1970}
 }
 
 @book{Conway:1995,
         address = {Berlin, Heidelberg, New York},
         author = {J.B. Conway},
         isbn = {0387944605},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Conway - Functions of One Complex Variable I.djvu},
         publisher = {Springer},
         title = {{Functions of one complex variable, Vol. II}},
         year = {1995}
 }
 
 @book{Boas:1954,
         author = {R.P. Boas},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Boas - Entire Functions.djvu},
         publisher = {Academic Press},
         title = {{Entire Functions}},
         year = {1954}
 }
 
 @article{RehrenSchroer:1987,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren and B. Schroer},
         journal = {Phys. Lett. B},
         localfile = {1987 - Rehren, Schroer - Exchange algebra on the lightcone and order-disorder 2n-point functions in the Ising field theory.pdf},
         pages = {84--88},
         title = {{Exchange algebra on the lightcone and order-disorder 2n-point functions in the Ising field theory}},
         volume = {198},
         year = {1987}
 }
 
 @article{SchroerTruong:1978,
         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]},
         author = {B. Schroer and T.T. Truong},
         journal = {Phys. Lett.},
         localfile = {1978 - Schroer, Truong - The Relativistic Quantum Fields of the d=2 Ising Model.pdf},
         number = {3},
         pages = {371--374},
         title = {{The Relativistic Quantum Fields of the d=2 Ising Model}},
         volume = {72 B},
         year = {1978}
 }
 
 @article{SchroerTruong:1977,
         author = {B. Schroer and T.T. Truong},
         journal = {Phys. Rev. D},
         localfile = {1977 - Schroer, Truong - Equivilance of the Sine-Gordon and Thirring models and cumulative mass effects.pdf},
         number = {6},
         pages = {1684--1693},
         title = {{Equivalence of the Sine-Gordon and Thirring models and cumulative mass effects}},
         volume = {15},
         year = {1977}
 }
 
 @article{SchroerTruong:1979,
         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.},
         author = {B. Schroer and T.T. Truong},
         journal = {Nucl. Phys. B},
         localfile = {1979 - Schroer, Truong - Z_2 Duality Algebra in d=2 Quantum Field Theory.pdf},
         pages = {125--139},
         title = {{Z2 Duality Algebra in d=2 Quantum Field Theory}},
         volume = {154},
         year = {1979}
 }
 
 @article{SchroerTruongWeisz:1979,
         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.},
         author = {B. Schroer and T.T. Truong and P. Weisz},
         journal = {Nucl. Phys. B},
         localfile = {1979 - Schroer, Truong, Weisz - Supersymmetric Ising Field Theory.pdf},
         pages = {140--156},
         title = {{Supersymmetric Ising Field Theory}},
         volume = {154},
         year = {1979}
 }
 
 @article{SchroerTruong:1978-1,
         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.},
         author = {B. Schroer and T.T. Truong},
         journal = {Nucl. Phys. B},
         localfile = {1978 - Schroer, Truong - The Order-Disorder Quantum Field Operators associated with the tw-dimensional Ising Model in the Continuum Limit.pdf},
         pages = {80--122},
         title = {{The Order-Disorder Quantum Field Operators associated with the tw-dimensional Ising Model in the Continuum Limit}},
         volume = {144},
         year = {1978}
 }
 
 @article{SchroerTruongWeisz:1976,
         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.},
         author = {B. Schroer and T.T. Truong and P. Weisz},
         journal = {Phys. Lett.},
         localfile = {1976 - Schroer, Truong, Weisz - Towards an Explicit Construction of the Sine-Gordon Field Theory.pdf},
         pages = {422--424},
         title = {{Towards an Explicit Construction of the Sine-Gordon Field Theory}},
         volume = {63 B},
         year = {1976}
 }
 
 @article{SchroerTruongWeisz:1976-1,
         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.},
         author = {B. Schroer and T.T. Truong and P. Weisz},
         journal = {Ann. Phys.},
         localfile = {1976 - Schroer, Truong - Model Study of Nonleading Mass Singularities I.pdf},
         pages = {156--169},
         title = {{Model Study of Nonleading Mass Singularities I}},
         volume = {102},
         year = {1976}
 }
 
 @article{SchroerTruong:1978-2,
         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].},
         author = {B. Schroer and T.T. Truong},
         journal = {Phys. Lett.},
         localfile = {1978 - Schroer, Truong - Direct Construction of the Quantum Field Operators of the d=2 Ising Model.pdf},
         number = {2},
         pages = {149--151},
         title = {{Direct Construction of the Quantum Field Operators of the d=2 Ising Model}},
         volume = {73 B},
         year = {1978}
 }
 
 @article{Strich:2008,
         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.},
         author = {R. Strich},
         doi = {10.1063/1.2838155},
         journal = {J. Math. Phys.},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {2008 - Strich - Passive States for Essential Observers.pdf},
         number = {022301},
         pdf = {http://arxiv.org/pdf/0801.3529},
         title = {{Passive States for Essential Observers}},
         url = {http://arxiv.org/abs/0801.3529},
         v1descr = {Wed, 23 Jan 2008 08:56:31 GMT (19kb)},
         volume = {49},
         year = {2008}
 }
 
 @article{Mund:2008,
         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.},
         author = {J. Mund},
         journal = {Commun. Math. Phys.},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         pages = {1159--1180},
         pdf = {http://arxiv.org/pdf/0801.3621},
         title = {{The Spin-Statistics Theorem for Anyons and Plektons in d=2+1}},
         url = {http://arxiv.org/abs/0801.3621},
         v1descr = {Wed, 23 Jan 2008 16:32:47 GMT (35kb)},
         v1url = {http://www.arxiv.org/abs/0801.3621v1},
         v2descr = {Fri, 18 Apr 2008 12:20:08 GMT (35kb)},
         volume = {286},
         year = {2009}
 }
 
 @techreport{IlievaThirring:1999,
         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.},
         author = {N. Ilieva and W. Thirring},
         journal = {Theor.Math.Phys. 121 (1999) 1294-1314; Teor.Mat.Fiz. 121 (1999) 40-65},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {1999 - Ilieva, Thirring - Anyons and the Bose-Fermi duality in the finite-temperature Thirring model.pdf},
         month = jun,
         number = {Vienna preprint UWThPh-1999-37, ESI preprint ESI-720-1999},
         pdf = {http://arxiv.org/pdf/math-ph/9906020},
         title = {{Anyons and the Bose-Fermi duality in the finite-temperature Thirring model}},
         url = {http://arxiv.org/abs/math-ph/9906020},
         v1descr = {Wed, 23 Jun 1999 14:44:45 GMT (25kb)},
         year = {1999}
 }
 
 @article{Cuntz:1977,
         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.},
         author = {J. Cuntz},
         journal = {Commun. Math. Phys.},
         localfile = {1977 - Cuntz - Simple Cstar-algebras generated by isometries.pdf},
         pages = {173--185},
         title = {{Simple C*-Algebras Generated by Isometries}},
         volume = {57},
         year = {1977}
 }
 
 @article{Longo:1997,
         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.},
         author = {R. Longo},
         eprint = {gr-qc/9605073},
         journal = {Commun. Math. Phys.},
         pages = {451--479},
         slaccitation = {\%\%CITATION = GR-QC/9605073\\;\%\%},
         title = {{An analogue of the Kac-Wakimoto formula and black hole conditional entropy}},
         url = {http://arxiv.org/abs/gr-qc/9605073},
         volume = {186},
         year = {1997}
 }
 
 @misc{Summers:2005,
         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.},
         author = {S. J. Summers},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2005 - Summers - Tomita-Takesaki Modular Theory.pdf},
         month = nov,
         pdf = {http://arxiv.org/pdf/math-ph/0511034},
         title = {{Tomita-Takesaki Modular Theory}},
         url = {http://arxiv.org/abs/math-ph/0511034},
         v1descr = {Wed, 9 Nov 2005 19:14:09 GMT (12kb)},
         year = {2005}
 }
 
 @article{Araki:1976,
         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.},
         author = {H. Araki},
         journal = {Publ. RIMS, Kyoto University},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {1975 - Araki - Relative entropy of states of von Neumann algebras.pdf},
         number = {11},
         pages = {809--833},
         title = {{Relative Entropy of States of von Neumann Algebras}},
         year = {1976}
 }
 
 @article{Araki:1977,
         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.},
         author = {H. Araki},
         journal = {Publ. RIMS, Kyoto University},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {1977 - Araki - Relative entropy for states of von Neumann algebras II.pdf},
         number = {13},
         pages = {173--192},
         title = {{Relative Entropy of States of von Neumann Algebras II}},
         year = {1977}
 }
 
 @article{EckmannFrhlich:1974,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{J.-P.}}}}}}}}}}}}}}}}}}}}}}}}} Eckmann and J. Fr{\"{o}}hlich},
         journal = {Annales Henri Poincare},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {1974 - Eckmann, Fr\"{o}hlich - Unitary equivalence of local algebras in the quasifree representation.pdf},
         number = {2},
         pages = {201--209},
         title = {{Unitary equivalence of local algebras in the quasifree representation }},
         volume = {20},
         year = {1974}
 }
 
 @article{BuchholzSummers:1992,
         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.},
         author = {D. Buchholz and S. J. Summers},
         journal = {Commun. Math. Phys.},
         localfile = {1993 - Buchholz, Summers - An algebraic characterization of vacuum states in Minkowski space.pdf},
         pages = {449--458},
         title = {{An Algebraic Characterization of Vacuum States in Minkowski Space }},
         volume = {155},
         year = {1992}
 }
 
 @article{Langmann:1994,
         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,},
         author = {E. Langmann},
         journal = {Commun. Math. Phys.},
         localfile = {1994 - Langmann - Fermion current algebras and Schwinger terms in (3+1)-dimensions.pdf},
         pages = {1--32},
         title = {{Fermion Current Algebras and Schwinger Terms in (3 + 1)-Dimensions }},
         volume = {162},
         year = {1994}
 }
 
 @article{LongoRehren:1995,
         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.},
         author = {R. Longo and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         journal = {Rev. Math. Phys.},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {1994 - Longo, Rehren - Nets of Subfactors.pdf},
         pages = {567--598},
         title = {{Nets of Subfactors}},
         volume = {7},
         year = {1995}
 }
 
 @article{MundSchrader:1994,
         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.},
         author = {J. Mund and R. Schrader},
         journal = {Preprint},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {1994 - Mund, Schrader - Hilbert Spaces for Nonrelativistic and Relativistic Free Plektons (Particles with Braid Group Statistics).pdf},
         title = {{Hilbert Spaces for Nonrelativistic and Relativistic ``Free'' Plektons (Particles with Braid Group Statistics)}},
         year = {1994}
 }
 
 @article{Jr:1996-1,
         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.},
         author = {M. J{\"{o}}r{\ss}},
         journal = {Lett. Math. Phys.},
         localfile = {1995 - J\"{o}r{\ss} - The Construction of Pointlike Localized Charged Fields from Conformal Haag-Kastler Nets.pdf},
         pages = {257--274},
         title = {{The Construction of Pointlike Localized Charged Fields from Conformal Haag-Kastler Nets}},
         url = {http://arxiv.org/abs/hep-th/9506016},
         volume = {38},
         year = {1996}
 }
 
 @article{LiguoriMintchev:1995,
         abstract = {Fock representations for quantum fields which obey generalized statistics are explicitly constructed. The main features of these representations are investigated.},
         author = {A. Liguori and M. Mintchev},
         journal = {Lett. Math. Phys.},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {1995 - Liguori, Mintchev - Fock Spaces with Generalized Statistics.pdf},
         pages = {283--295},
         title = {{Fock Spaces with Generalized Statistics}},
         volume = {33},
         year = {1995}
 }
 
 @article{BalogNiedermaierHauer:1996,
         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 $100m$.},
         author = {J. Balog and M. R. Niedermaier and T. Hauer},
         journal = {Phys. Lett. B},
         localfile = {1996 - Balog, Niedermaier, Hauer - Perturbative versus Non-perturbative QFT Lessons from the O(3) NLS Model.pdf},
         pages = {224--232},
         title = {{Perturbative versus Non-perturbative QFT -- Lessons from the O(3) NLS Model}},
         url = {http://arxiv.org/abs/hep-th/9604161},
         volume = {386},
         year = {1996}
 }
 
 @article{Filk:1996,
         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.},
         author = {T. Filk},
         journal = {Phys. Lett. B},
         keywords = {NCQFT},
         localfile = {1996 - Filk - Divergenices of a field theory on quantum space.pdf},
         pages = {53--58},
         title = {{Divergencies in a field theory on quantum space}},
         volume = {376},
         year = {1996}
 }
 
 @article{GrosseLangmannRaschhofer:1997,
         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.},
         author = {H. Grosse and E. Langmann and E. Raschhofer},
         journal = {Annals Phys.},
         localfile = {1996 - Grosse, Langmann, Raschhofer - The Luttinger--Schwinger Model.pdf},
         pages = {310--331},
         title = {{The Luttinger-Schwinger Model}},
         url = {http://arxiv.org/abs/hep-th/9609206},
         volume = {253},
         year = {1997}
 }
 
 @article{Borchers:1997-1,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Preprint},
         localfile = {1997 - Borchers - Half-sided Translations in Connection with Modular Groups as a Tool in Quantum Field Theory.pdf},
         title = {{Half--sided Translations in Connection with Modular Groups as a Tool in Quantum Field Theory }},
         year = {1997}
 }
 
 @phdthesis{Mger:1997,
         author = {M. M{\"{u}}ger},
         localfile = {1997 - M\"{u}ger - Superselection Structure of Quantum Field Theories in 1+1 Dimenions PhD.pdf},
         school = {Hamburg},
         title = {{Superselection structure of quantum field theories in 1+1 dimensions}},
         year = {1997}
 }
 
 @article{Schroer:1997,
         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.},
         author = {B. Schroer},
         journal = {Nucl. Phys. B},
         localfile = {1997 - Schroer - Wigner Representation Theory of the Poincare Group, Localization, Statistics and the S-Matrix.pdf},
         pages = {519--546},
         title = {{Wigner Representation Theory of the Poincare Group, Localization, Statistics and the S-Matrix}},
         url = {http://arxiv.org/abs/hep-th/9608092},
         volume = {499},
         year = {1997}
 }
 
 @phdthesis{Wulkenhaar:1997,
         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.},
         author = {R. Wulkenhaar},
         localfile = {1997 - Wulkenhaar - Non-Associative Geometry - Unified Models Based on L-Cycles -- PhD Thesis.pdf},
         school = {Leipzig},
         title = {{Non--Associative Geometry - Unified Models Based on L--Cycles }},
         year = {1997}
 }
 
 @article{Dorey:1998,
         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.},
         author = {P. Dorey},
         journal = {Preprint},
         localfile = {1998 - Dorey - Exact S-matrices.pdf},
         title = {{Exact S-matrices}},
         url = {http://arxiv.org/abs/hep-th/9810026},
         year = {1998}
 }
 
 @article{EvesonFewster:1998,
         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.},
         author = {S. P. Eveson and C. J. Fewster},
         journal = {Phys. Rev. D},
         localfile = {1998 - Eveson, Fewster - Bounds on negative energy densities in flat spacetime.pdf},
         title = {{Bounds on negative energy densities in flat spacetime}},
         volume = {58},
         year = {1998}
 }
 
 @article{Schroer:1998,
         author = {B. Schroer},
         journal = {Preprint},
         localfile = {1998 - Schroer - Localization and Nonperturbative Local Quantum Physics.pdf},
         title = {{A Course On: Modular Localization and Non-Perturbative Local Quantum Physics}},
         year = {1998}
 }
 
 @article{Schroer:1999,
         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.},
         author = {B. Schroer},
         journal = {Annals Phys.},
         localfile = {1998 - Schroer - Modular Wedge Localization and the d=1+1 Formfactor Program.pdf},
         pages = {190--223},
         title = {{Modular Wedge Localization and the d=1+1 Formfactor Program}},
         url = {http://arxiv.org/abs/hep-th/9712124},
         volume = {275},
         year = {1999}
 }
 
 @article{Wassermann:1998,
         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.},
         author = {A. Wassermann},
         journal = {Preprint},
         localfile = {1998 - Wassermann - OPERATOR ALGEBRAS AND CONFORMAL FIELD THEORY III.pdf},
         title = {{Operator Algebras and Conformal Field Theory III. Fusion of positive }},
         url = {http://arxiv.org/abs/math/9806031},
         year = {1998}
 }
 
 @phdthesis{Florig:1999,
         author = {M. Florig},
         localfile = {1999 - Florig - Geometric Modular Action -- PhD-Thesis.pdf},
         school = {Gainesville},
         title = {{Geometric Modular Action}},
         year = {1999}
 }
 
 @article{Oeckl:2001,
         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.},
         author = {R. Oeckl},
         journal = {Commun. Math. Phys.},
         localfile = {1999 - Oeckl - Braided Quantum Field Theory.pdf},
         pages = {451--473},
         title = {{Braided Quantum Field Theory}},
         url = {http://arxiv.org/abs/hep-th/9906225},
         volume = {217},
         year = {2001}
 }
 
 @article{Schroer:2000,
         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.},
         author = {B. Schroer},
         journal = {J. Phys. A},
         localfile = {1999 - Schroer - New Concepts in Particle Physics from Solution of an Old Problem.pdf},
         pages = {5231},
         title = {{New Concepts in Particle Physics from Solution of an Old Problem}},
         url = {http://arxiv.org/abs/hep-th/9908021},
         volume = {33},
         year = {2000}
 }
 
 @phdthesis{Bostelmann:2000,
         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.},
         author = {H. Bostelmann},
         localfile = {2000 - Bostelmann - Lokale Algebren und Operatorprodukte am Punkt.pdf},
         school = {G\"{o}ttingen},
         title = {{Lokale Algebren und Operatorprodukte am Punkt}},
         year = {2000}
 }
 
 @misc{CareyPhillipsRennie:2008,
         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.},
         author = {A. L. Carey and J. Phillips and A. Rennie},
         keywords = {K-Theory and Homology (math.KT); Operator Algebras (math.OA)},
         localfile = {2008 - Carey, Phillips, Rennie - Twisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras.pdf},
         month = jan,
         pdf = {http://arxiv.org/pdf/0801.4605},
         title = {{Twisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras}},
         url = {http://arxiv.org/abs/0801.4605},
         v1descr = {Wed, 30 Jan 2008 05:47:03 GMT (45kb)},
         year = {2008}
 }
 
 @misc{CareyRennieTong:2008,
         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.},
         author = {A. L. Carey and A. Rennie and K. Tong},
         keywords = {Operator Algebras (math.OA); Quantum Algebra (math.QA)},
         month = feb,
         pdf = {http://arxiv.org/pdf/0802.0317},
         title = {{Spectral flow invariants and twisted cyclic theory from the Haar state on SU\_q(2)}},
         url = {http://arxiv.org/abs/0802.0317},
         v1descr = {Mon, 4 Feb 2008 00:15:53 GMT (35kb)},
         year = {2008}
 }
 
 @misc{Summers:2008,
         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.},
         author = {S. J. Summers},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {2008 - Summers - Yet More Ado About Nothing: The Remarkable Relativistic Vacuum State.pdf},
         month = feb,
         pdf = {http://arxiv.org/pdf/0802.1854},
         title = {{Yet More Ado About Nothing: The Remarkable Relativistic Vacuum State}},
         url = {http://arxiv.org/abs/0802.1854},
         v1descr = {Wed, 13 Feb 2008 15:58:09 GMT (29kb)},
         year = {2008}
 }
 
 @misc{Schroer:2008,
         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.},
         author = {B. Schroer},
         keywords = {Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
         localfile = {2008 - Schroer - Is inert matter from indecomposable positive energy infinite spin representations the much sought-after dark matter.pdf},
         month = feb,
         pdf = {http://arxiv.org/pdf/0802.2098},
         title = {{Is inert matter from indecomposable positive energy ``infinite spin'' representations the much sought-after dark matter?}},
         url = {http://arxiv.org/abs/0802.2098},
         v1descr = {Thu, 14 Feb 2008 20:40:40 GMT (14kb)},
         v1url = {http://www.arxiv.org/abs/0802.2098v1},
         v2descr = {Fri, 15 Feb 2008 10:30:28 GMT (15kb)},
         year = {2008}
 }
 
 @article{Verch:1993,
         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.},
         author = {R. Verch},
         journal = {Lett. Math. Phys.},
         keywords = {Mathematical Physics (math-ph); QFT on curved spacetime},
         localfile = {1993 - Verch - Antilocality and a Reeh-Schlieder Theorem on Manifolds.pdf},
         pages = {143--154},
         title = {{Antilocality and a Reeh-Schlieder Theorem on Manifolds}},
         volume = {28},
         year = {1993}
 }
 
 @misc{Summers:2008-1,
         abstract = {Assertions made in a document recently deposited in the arXiv are refuted.},
         author = {S. J. Summers},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {2008 - Summers - ``On the Impossibility of a Poincare-Invariant Vacuum State with Unit Norm'' Refuted.pdf},
         month = feb,
         pdf = {http://arxiv.org/pdf/0802.2935},
         title = {{``On the Impossibility of a Poincare-Invariant Vacuum State with Unit Norm'' Refuted}},
         url = {http://arxiv.org/abs/0802.2935},
         v1descr = {Wed, 20 Feb 2008 20:29:54 GMT (5kb)},
         year = {2008}
 }
 
 @misc{Berkowitz:2008,
         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.},
         author = {J. Berkowitz},
         keywords = {Crackpot Stuff},
         month = feb,
         pdf = {http://arxiv.org/pdf/0802.0216},
         title = {{On the Impossibility of a Poincare-invariant Vacuum State with Unit Norm}},
         url = {http://arxiv.org/abs/0802.0216},
         v1descr = {Fri, 1 Feb 2008 22:40:04 GMT (47kb)},
         v1url = {http://www.arxiv.org/abs/0802.0216v1},
         v2descr = {Thu, 7 Feb 2008 03:19:01 GMT (47kb)},
         year = {2008}
 }
 
 @article{Longo:1989,
         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.},
         author = {R. Longo},
         journal = {Commun. Math. Phys.},
         localfile = {1989 - Longo - Index of subfactors and statistics of quantum fields I.pdf},
         pages = {217--247},
         title = {{Index of subfactors and statistics of quantum fields I}},
         volume = {126},
         year = {1989}
 }
 
 @article{MackSchomerus:1990,
         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.},
         author = {G. Mack and V. Schomerus},
         journal = {Commun. Math. Phys.},
         localfile = {1990 - Mack, Schomerus - Conformal field algebras with quantum symmetry from the theory of superselection sectors.pdf},
         pages = {139--196},
         title = {{Conformal Field Algebras with Quantum Symmetry from the Theory of Superselection Sectors }},
         volume = {134},
         year = {1990}
 }
 
 @article{Jaffe:2000,
         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.},
         author = {A. Jaffe},
         journal = {Preprint},
         localfile = {2000 - Jaffe - Constructive Quantum Field Theory.pdf},
         title = {{Constructive Quantum Field Theory}},
         year = {2000}
 }
 
 @article{Schroer:1999-1,
         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.},
         author = {B. Schroer},
         journal = {Preprint},
         localfile = {1999 - Schroer - New Concepts in Particle Physics from Solution of an Old Problem.pdf},
         title = {{Particle Physics and QFT at the Turn of the Century Old principles with new concepts (an essay on local quantum physics) }},
         year = {1999}
 }
 
 @article{Varadarajan:2000,
         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.},
         author = {M. Varadarajan},
         journal = {Phys.Rev. D},
         keywords = {General Relativity and Quantum Cosmology (gr-qc)},
         localfile = {2000 - Varadarajan - Fock representations from U(1) holonomy algebras.pdf},
         month = jan,
         pages = {104001},
         pdf = {http://arxiv.org/pdf/gr-qc/0001050},
         title = {{Fock representations from U(1) holonomy algebras}},
         url = {http://arxiv.org/abs/gr-qc/0001050},
         v1descr = {Wed, 19 Jan 2000 09:02:52 GMT (21kb)},
         volume = {61},
         year = {2000}
 }
 
 @article{Borchers:1998,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Lett. Math. Phys.},
         localfile = {1998 - Borchers - Half-sided Translations and the Type of von Neumann Algebras.pdf},
         pages = {283--290},
         title = {{Half-Sided Translations and the Type of von Neumann Algebras}},
         volume = {44},
         year = {1998}
 }
 
 @article{Fidaleo:2001,
         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.},
         author = {F. Fidaleo},
         journal = {Proc. Am. Math. Soc.},
         localfile = {2001 - Fidaleo - On the split property for inclusions of W-algebras.pdf},
         number = {1},
         pages = {121--127},
         title = {{On the Split Property for Inclusions of W*-Algebras}},
         volume = {130},
         year = {2001}
 }
 
 @article{EbrahimiFard:2002,
         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.},
         author = {K. Ebrahimi-Fard},
         journal = {J. Phys. A},
         localfile = {2002 - Ebrahimi-Fard - On the relation between modular theory and geometry.pdf},
         pages = {6319--6328},
         title = {{On the relation between modular theory and geometry }},
         volume = {35},
         year = {2002}
 }
 
 @article{Ojima:1981,
         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.},
         author = {I. Ojima},
         journal = {Ann. Phys.},
         localfile = {1981 - Ojima - Gauge Fields at Finite Temperature - ``Thermo Field Dynamics'' and the KMS Condition and Their Extension to Gauge Theories.pdf},
         pages = {1--32},
         title = {{Gauge Fields at Finite Temperature - ``Thermo Field Dynamics'' and the KMS Condition and Their Extension to Gauge Theories}},
         volume = {137},
         year = {1981}
 }
 
 @phdthesis{Zahn:2007,
         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.},
         author = {J. Zahn},
         keywords = {NC Minkowski; NCQFT},
         localfile = {2007 - Zahn - Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space - PhD-Thesis.pdf},
         school = {Hamburg},
         title = {{Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space }},
         year = {2007}
 }
 
 @article{KopfPaschke:2007,
         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. ˙},
         author = {T. Kopf and M. Paschke},
         journal = {Preprint},
         localfile = {2007 - Kopf, Paschke - Generally covariant quantum mechanics on noncommutative configuration spaces.pdf},
         title = {{Generally covariant quantum mechanics on noncommutative configuration spaces }},
         year = {2007}
 }
 
 @article{Dybalski:2007,
         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.},
         author = {W. Dybalski},
         journal = {Preprint},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {2007 - Dybalski - A sharpened nuclearity condition and the uniqueness of the vacuum in QFT.pdf},
         title = {{A sharpened nuclearity condition and the uniqueness of the vacuum in QFT }},
         year = {2007}
 }
 
 @article{MundKuckert:2004,
         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.},
         author = {J. Mund and B. Kuckert},
         journal = {Preprint},
         localfile = {2004 - Kuckert, Mund - Spin and Statistics in Nonrelativistic Quantum Mechanics II.pdf},
         title = {{Spin \& Statistics in Nonrelativistic Quantum Mechanics, II }},
         year = {2004}
 }
 
 @article{Tureanu:2007,
         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.},
         author = {A. Tureanu},
         journal = {Preprint},
         keywords = {NCQFT},
         localfile = {2007 - Tureanu - Twisted Poincare Symmetry and Some Implications on Noncommutative Quantum Field Theory.pdf},
         title = {{Twisted Poincare Symmetry and Some Implications on Noncommutative Quantum Field Theory}},
         year = {2007}
 }
 
 @article{tHooft:2007,
         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.},
         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},
         journal = {Preprint},
         localfile = {2007 - t'Hooft - The Grand Views of Physics.pdf},
         title = {{The Grand View of Physics}},
         year = {2007}
 }
 
 @article{BrunettiFredenhagenVerch:2001,
         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.},
         author = {R. Brunetti and K. Fredenhagen and R. Verch},
         doi = {10.1007/s00220-003-0815-7},
         journal = {Commun. Math. Phys.},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2001 - Brunetti, Fredenhagen, Verch - The generally covariant locality principle - A new paradigm for local quantum physics.pdf},
         pages = {31--68},
         pdf = {http://arxiv.org/pdf/math-ph/0112041},
         title = {{The generally covariant locality principle -- A new paradigm for local quantum physics}},
         url = {http://arxiv.org/abs/math-ph/0112041},
         v1descr = {Wed, 19 Dec 2001 10:35:59 GMT (63kb)},
         volume = {237},
         year = {2003}
 }
 
 @phdthesis{Camassa:2003,
         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.},
         author = {P. Camassa},
         localfile = {2003 - Camassa - Quasi-Free States and KMS States of the Scalar Free Field.pdf},
         school = {Rome},
         title = {{Quasi-Free States and KMS States of the Free Scalar Field}},
         year = {2003}
 }
 
 @phdthesis{CastroAlvaredo:2001,
         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.},
         author = {O. Castro-Alvaredo},
         keywords = {Form Factor Program},
         localfile = {2001 - Castro-Alvaredo - Bootstrap Methods in 1+1-Dimensional Quantum Field Theories - the Homogeneous Sine-Gordon Models - PhD thesis.pdf},
         school = {Santiago de Compostela},
         title = {{Bootstrap Methods in 1+1-Dimensional Quantum Field Theories: the Homogeneous Sine-Gordon Models }},
         url = {http://www.staff.city.ac.uk/o.castro-alvaredo/heptese.pdf},
         year = {2001}
 }
 
 @lecturenotes{Schroer:2001,
         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.},
         author = {B. Schroer},
         localfile = {2001 - Schroer - Lectures on Algebraic Quantum Field Theory and Operator Algebras.pdf},
         school = {Florianopolis, Rio de Janeiro},
         title = {{Lectures on Algebraic Quantum Field Theory and Operator Algebras}},
         year = {2001}
 }
 
 @mastersthesis{Kniemeyer:2002,
         author = {O. Kniemeyer},
         localfile = {2002 - Kniemeyer - Untersuchungen am erzeugenden Funktional der AdS-CFT-Korrespondenz.pdf},
         school = {G\"{o}ttingen},
         title = {{Untersuchungen am erzeugenden Funktional der AdS-CFT-Korrespondenz}},
         year = {2002}
 }
 
 @article{KawahigashiLongo:2003,
         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.},
         author = {Y. Kawahigashi and R. Longo},
         journal = {Preprint},
         localfile = {2003 - Kawahigashi, Longo - Classification of Two-dimensional Local Conformal Nets with c smaller 1 and 2-cohomology Vanishing for Tensor Categories.pdf},
         title = {{Classification of Two-dimensional Local Conformal Nets with c < 1 and 2-cohomology Vanishing for Tensor Categories}},
         year = {2003}
 }
 
 @article{BuchholzSummers:2004,
         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.},
         author = {D. Buchholz and S. J. Summers},
         journal = {Preprint},
         localfile = {2004 - Buchholz, Summers - Quantum statistics and locality.pdf},
         title = {{Quantum Statistics and Locality }},
         year = {2004}
 }
 
 @article{ChaichianPresnajderTureanu:2004,
         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.},
         author = {M. Chaichian and P. Presnajder and A. Tureanu},
         journal = {Preprint},
         keywords = {NCQFT},
         localfile = {© symmetry and its implications.pdf},
         title = {{New concept of relativistic invariance in NC space-time: twisted Poincare symmetry and its implications}},
         year = {2004}
 }
 
 @article{FewsterOjimaPorrmann:2004,
         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.},
         author = {C. J. Fewster and I. Ojima and M. Porrmann},
         journal = {Preprint},
         localfile = {2004 - Fewster, Ojima, Porrmann - p-Nuclearity in a New Perspective.pdf},
         title = {{p-Nuclearity in a New Perspective}},
         year = {2004}
 }
 
 @article{HeslopSibold:2005,
         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.},
         author = {P. Heslop and K. Sibold},
         journal = {Preprint},
         localfile = {2004 - Heslop, Sibold - Quantized equations of motion in non-commutative theories.pdf},
         title = {{Quantized equations of motion in non-commutative theories}},
         year = {2005}
 }
 
 @article{MundSchroerYngvason:2004,
         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.},
         author = {J. Mund and B. Schroer and J. Yngvason},
         journal = {Phys.Lett. B},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2004 - Mund, Schroer, Yngvason - String-Localized quantum fields from Wigner representations.pdf},
         pages = {156--162},
         pdf = {http://arxiv.org/pdf/math-ph/0402043},
         title = {{String-localized quantum fields from Wigner representations}},
         url = {http://arxiv.org/abs/math-ph/0402043},
         v1descr = {Mon, 16 Feb 2004 22:56:27 GMT (10kb)},
         v1url = {http://www.arxiv.org/abs/math-ph/0402043v1},
         v2descr = {Sat, 29 May 2004 13:52:34 GMT (13kb)},
         volume = {596},
         year = {2004}
 }
 
 @article{Ullrich:2004-1,
         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},
         author = {P. Ullrich},
         journal = {Preprint},
         localfile = {2004 - Ullrich - Uniqueness in the Characteristic Cauchy Problem of the Klein-Gordon Equation and Tame Restrictions of Generalized Functions.pdf},
         title = {{Uniqueness in the Characterisitc Cauchy Problem of the Klein-Gordon Equation and Tame Restrictions of Generalized Functions}},
         year = {2004}
 }
 
 @article{Gallavotti:2005,
         author = {G. Gallavotti},
         journal = {Preprint},
         keywords = {Constructive Quantum Field Theory},
         localfile = {2005 - Gallavotii - Constructive Quantum Field Theory.pdf},
         title = {{Constructive Quantum Field Theory}},
         year = {2005}
 }
 
 @article{DAntoniMorsella:2006,
         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.},
         author = {C. D'Antoni and G. Morsella},
         journal = {Preprint},
         keywords = {Algebraic Quantum Field Theory},
         localfile = {2006 - D'Antoni, Morsella - Scaling algebras and superselection sectors: Study of a class of models.pdf},
         title = {{Scaling Algebras and Superselection Sectors: Study of a Class of Models }},
         year = {2006}
 }
 
 @article{Fleischhack:2006,
         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.},
         author = {C. Fleischhack},
         journal = {Preprint},
         keywords = {Loop Quantum Gravity},
         localfile = {2006 - Fleischhack - Kinematical Uniqueness of Loop Quantum Gravity.pdf},
         title = {{Kinematical Uniqueness of Loop Quantum Gravity }},
         year = {2006}
 }
 
 @article{GieselThiemann:2006,
         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.},
         author = {K. Giesel and T. Thiemann},
         journal = {Preprint},
         keywords = {Loop Quantum Gravity},
         localfile = {2006 - Giesel, Thiemann - Algebraic Quantum Gravity (AQG) I. Conceptual Setup.pdf},
         title = {{Algebraic Quantum Gravity (AQGI I. Conceptual Setup }},
         year = {2006}
 }
 
 @article{KawahigashiLongoPennigRehren:2006,
         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.},
         author = {Y. Kawahigashi and R. Longo and U. Pennig and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         journal = {Preprint},
         keywords = {Algebraic Quantum Field Theory; Conformal Quantum Field Theory},
         localfile = {2006 - Kawahigashi, Longo, Pennig, Rehren - The classification of non-local chiral CFT with c less than 1.pdf},
         title = {{The classification of non-local chiral CFT with c<1}},
         year = {2006}
 }
 
 @article{KaminskiLewandowskiOkolow:2006,
         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.},
         author = {W. Kaminski and J. Lewandowski and A. Okolow},
         journal = {Preprint},
         keywords = {Loop Quantum Gravity},
         localfile = {2006 - Lewandowski, Kaminski, Okolow - Background independent quantizations: the scalar field II.pdf},
         title = {{Background independent quantizations: the scalar field II}},
         year = {2006}
 }
 
 @article{RedeiSummers:2006,
         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.},
         author = {M. Redei and S. J. Summers},
         journal = {Preprint},
         localfile = {2006 - Redei, Summers - Quantum Probability Theory.pdf},
         title = {{Quantum Probability Theory}},
         year = {2006}
 }
 
 @article{Sahlmann:2006,
         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.},
         author = {H. Sahlmann},
         journal = {Preprint},
         keywords = {Loop Quantum Gravity},
         localfile = {2006 - Sahlmann - Exploring the diffeomorphism invariant Hilbert space of a scalar field.pdf},
         title = {{Exploring the diffeomorphism invariant Hilbert space of a scalar field }},
         year = {2006}
 }
 
 @article{Thiemann:2006,
         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.},
         author = {T. Thiemann},
         journal = {Preprint},
         keywords = {Loop Quantum Gravity; popular science},
         localfile = {2006 - Thiemann - Ein Universum aus brodelnden Schleifen.pdf},
         title = {{Ein Universum aus brodelnden Schleifen}},
         year = {2006}
 }
 
 @article{Thiemann:2006-1,
         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.},
         author = {T. Thiemann},
         journal = {Preprint},
         keywords = {Loop Quantum Gravity},
         localfile = {2006 - Thiemann - Loop Quantum Gravity - An Inside View.pdf},
         title = {{Loop Quantum Gravity: An Inside View}},
         year = {2006}
 }
 
 @article{BalogWeisz:2007,
         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.},
         author = {J. Balog and P. Weisz},
         journal = {Preprint},
         keywords = {Form Factor Program; kw:sigma},
         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},
         title = {{Construction and clustering properties of the 2-d non--linear σ--model form factors: O(3), O(4), large n examples}},
         year = 2007
 }
 
 @article{Baumgrtner:2007,
         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.},
         author = {B. Baumg{\"{a}}rtner},
         journal = {Preprint},
         localfile = {2007 - Baumg\"{a}rtner - Thermodynamic Stability: A note on a footnote in Ruelle's book.pdf},
         title = {{Thermodynamic Stability - A note on a footnote in Ruelle{\rq}s book }},
         year = {2007}
 }
 
 @article{Dybalski:2008,
         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.},
         author = {W. Dybalski},
         journal = {Lett.Math.Phys.},
         keywords = {Algebraic Quantum Field Theory; Mathematical Physics (math-ph)},
         pages = {217--230},
         pdf = {http://arxiv.org/pdf/0803.1468},
         title = {{A sharpened nuclearity condition for massless fields}},
         url = {http://arxiv.org/abs/0803.1468},
         v1descr = {Mon, 10 Mar 2008 18:05:55 GMT (15kb)},
         v1url = {http://www.arxiv.org/abs/0803.1468v1},
         v2descr = {Tue, 8 Jul 2008 13:04:54 GMT (15kb)},
         volume = {84},
         year = {2008}
 }
 
 @article{BaumgrtelJurkeLled:1995,
         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.},
         author = {H. Baumg{\"{a}}rtel and M. Jurke and F. Lled{\'{o}}},
         doi = {10.1016/0034-4877(96)83512-9},
         journal = {Rept. Math. Phys.},
         localfile = {1995 - Baumg\"{a}rtel, Jurke, Lled\'{o} - On Free Nets Over Minkowski Space.pdf},
         number = {1},
         pages = {101--127},
         title = {{On Free Nets Over Minkowski Space}},
         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},
         volume = {35},
         year = {1995}
 }
 
 @article{EckmannOsterwalder:1973,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{J.-P.}}}}}}}}}}}}}}}}}}}}}}}}} Eckmann and K. Osterwalder},
         doi = {10.1016/0022-1236(73)90062-1},
         journal = {J. Funct. Anal.},
         keywords = {Modular Theory},
         localfile = {1972 - Eckmann, Osterwalder - An application of Tomita's theory of modular Hilbert algebras: Duality for free Bose fields.pdf},
         number = {1},
         pages = {1--12},
         title = {{An application of Tomita's theory of modular Hilbert algebras: Duality for free Bose fields}},
         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},
         volume = {13},
         year = {1973}
 }
 
 @misc{Kopper:2005,
         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.},
         author = {C. Kopper},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2005 - Kopper - Renormalization Theory based on Flow Equations.pdf},
         month = aug,
         pdf = {http://arxiv.org/pdf/hep-th/0508143},
         title = {{Renormalization Theory based on Flow Equations}},
         url = {http://arxiv.org/abs/hep-th/0508143},
         v1descr = {Fri, 19 Aug 2005 19:09:01 GMT (17kb)},
         year = {2005}
 }
 
 @article{KleinLandau:1982,
         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.},
         author = {A. Klein and L. J. Landau},
         journal = {Commun. Math. Phys.},
         keywords = {kw:NC-Wick},
         localfile = {1983 - Klein, Landau - From the Euclidean group to the Poincar\'{e} group via Osterwalder-Schrader positivity.pdf},
         pages = {469--484},
         title = {{From the Euclidean group to the Poincar\'{e} group via Osterwalder-Schrader positivity}},
         url = {http://projecteuclid.org/euclid.cmp/1103922129},
         volume = {87},
         year = {1982}
 }
 
 @article{LscherMack:1975,
         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 ... .},
         author = {M. L{\"{u}}scher and G. Mack},
         journal = {Commun. Math. Phys.},
         localfile = {1975 - L\"{u}scher, Mack - Global Conformal Invariance in Quantum Field Theory.pdf},
         pages = {203--234},
         title = {{Global conformal invariance in quantum field theory}},
         url = {http://projecteuclid.org/euclid.cmp/1103898909},
         volume = {41},
         year = {1975}
 }
 
 @phdthesis{Paschke:2001,
         author = {M. Paschke},
         localfile = {2001 - Paschke - Von Nichtkommutativen Geometrien, ihren Symmetrien und etwas Hochenergiephysik.pdf},
         school = {Mainz},
         title = {{Von nichtkommutativen Geometrien, ihren Symmetrien und etwas Hochenergiephysik}},
         year = {2001}
 }
 
 @misc{Schroer:2008-1,
         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.},
         author = {B. Schroer},
         journal = {Preprint},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2008 - Schroer - A note on Infraparticles and Unparticles.pdf},
         month = apr,
         pdf = {http://arxiv.org/pdf/0804.3563},
         title = {{A note on Infraparticles and Unparticles}},
         url = {http://arxiv.org/abs/0804.3563},
         v1descr = {Tue, 22 Apr 2008 19:35:38 GMT (6kb)},
         year = {2008}
 }
 
 @article{GuidoLongo:1992,
         author = {D. Guido and R. Longo},
         doi = {10.1007/BF02096548},
         journal = {Commun. Math. Phys.},
         keywords = {Algebraic Quantum Field Theory},
         localfile = {1992 - Guido, Longo - Relativistic invariance and charge conjugation in quantum field theory.pdf},
         pages = {521--551},
         slaccitation = {\%\%CITATION = CMPHA,148,521\\;\%\%},
         title = {{Relativistic invariance and charge conjugation in quantum field theory}},
         volume = {148},
         year = {1992}
 }
 
 @article{GayralGraciaBondiaIochumSchuckerVarilly:2004,
         archiveprefix = {arXiv},
         author = {V. Gayral and J. M. Gracia-Bondia and B. Iochum and T. Schucker and J. C. Varilly},
         doi = {10.1007/s00220-004-1057-z},
         eprint = {hep-th/0307241},
         journal = {Commun. Math. Phys.},
         keywords = {kw:NC-Wick},
         localfile = {2003 - Gayral, Gracia-Bondia, Iochum, Schucker, Varilly - Moyal planes are spectral triples.pdf},
         pages = {569--623},
         slaccitation = {\%\%CITATION = HEP-TH/0307241\\;\%\%},
         title = {{Moyal planes are spectral triples}},
         url = {http://arxiv.org/abs/hep-th/0307241},
         volume = {246},
         year = {2004}
 }
 
 @article{SwiecaVoelkel:1973,
         author = {J. A. Swieca and A. H. Voelkel},
         doi = {10.1007/BF01646134},
         journal = {Commun. Math. Phys.},
         localfile = {1973 - Swieca, V\"{o}lkel - Remarks on Conformal Invariance.pdf},
         pages = {319--342},
         slaccitation = {\%\%CITATION = CMPHA,29,319\\;\%\%},
         title = {{Remarks on conformal invariance}},
         url = {http://projecteuclid.org/euclid.cmp/1103858590},
         volume = {29},
         year = {1973}
 }
 
 @misc{Schroer:2008-2,
         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},
         author = {B. Schroer},
         keywords = {Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
         localfile = {2008 - Schroer - Do confinement and darkness have the same conceptual roots - The crucial role of localization.pdf},
         month = apr,
         pdf = {http://arxiv.org/pdf/0802.3526},
         title = {{Do confinement and darkness have the same conceptual roots? The crucial role of localization}},
         url = {http://arxiv.org/abs/0802.3526},
         v1descr = {Mon, 25 Feb 2008 14:48:20 GMT (19kb)},
         v1url = {http://www.arxiv.org/abs/0802.3526v1},
         v2descr = {Tue, 26 Feb 2008 16:22:21 GMT (21kb)},
         v2url = {http://www.arxiv.org/abs/0802.3526v2},
         v3descr = {Thu, 24 Apr 2008 18:51:52 GMT (31kb)},
         year = {2008}
 }
 
 @article{ChaichianNishijimaSalminenTureanu:2008,
         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.},
         author = {M. Chaichian and K. Nishijima and T. Salminen and A. Tureanu},
         journal = {JHEP},
         keywords = {High Energy Physics - Theory (hep-th); NCQFT},
         pages = {078},
         pdf = {http://arxiv.org/pdf/0805.3500},
         title = {{Noncommutative Quantum Field Theory: A Confrontation of Symmetries}},
         url = {http://arxiv.org/abs/0805.3500},
         v1descr = {Thu, 22 May 2008 16:47:02 GMT (19kb)},
         volume = {0806},
         year = {2008}
 }
 
 @article{Yngvason:1986,
         author = {J. Yngvason},
         journal = {Annales Poincare Phys. Theor.},
         keywords = {Algebraic Quantum Field Theory},
         localfile = {1986 - Yngvason - Invariant states on Borchers{\rq} tensor algebra.pdf},
         pages = {117--145},
         slaccitation = {\%\%CITATION = AHPAA,45,117\\;\%\%},
         title = {{Invariant states on Borchers' tensor algebra}},
         url = {http://www.numdam.org/numdam-bin/fitem?id=AIHPA_1986__45_2_117_0},
         volume = {45},
         year = {1986}
 }
 
 @article{Yngvason:1981,
         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.},
         author = {J. Yngvason},
         doi = {10.1007/BF01209075},
         journal = {Commun. Math. Phys.},
         keywords = {kw:NC-Wick},
         localfile = {1981 - Yngvason - Translationally invariant states and the spectrum ideal in the algebra of test functions for quantum fields.pdf},
         pages = {401},
         slaccitation = {\%\%CITATION = CMPHA,81,401\\;\%\%},
         title = {{Translationally invariant states and the spectrum ideal in the algebra of test functions for quantum fields}},
         url = {http://projecteuclid.org/euclid.cmp/1103920325},
         volume = {81},
         year = {1981}
 }
 
 @article{Yngvason:1973,
         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.},
         author = {J. Yngvason},
         doi = {10.1007/BF01646476},
         journal = {Commun. Math. Phys.},
         localfile = {1973 - Yngvason - On the Algebra of Test Functions for Field Operators - Decomposition of Linear Functionals into Positive Ones.pdf},
         pages = {315--333},
         slaccitation = {\%\%CITATION = CMPHA,34,315\\;\%\%},
         title = {{On the algebra of test functions for field operators. decomposition of linear functionals into positive ones}},
         url = {http://projecteuclid.org/euclid.cmp/1103859476},
         volume = {34},
         year = {1973}
 }
 
 @article{Borchers:1962,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         doi = {10.1007/BF02745645},
         journal = {Nuovo Cimento},
         keywords = {kw:NC-Wick},
         localfile = {1962 - Borchers - On Structure of the Algebra of Field Operators.pdf},
         title = {{On Structure of the Algebra of Field Operators}},
         volume = {24},
         year = {1962}
 }
 
 @article{Franco:2005,
         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.},
         archiveprefix = {arXiv},
         author = {D. H. T. Franco},
         doi = {10.1088/0305-4470},
         druck = {Booklet 22.07.08},
         eprint = {hep-th/0404029},
         journal = {J. Phys.},
         localfile = {2005 - Franco - On the Borchers Class of a Non-Commutative Field.pdf},
         pages = {5799--5808},
         slaccitation = {\%\%CITATION = HEP-TH/0404029\\;\%\%},
         title = {{On the Borchers class of a non-commutative field}},
         volume = {A38},
         year = {2005}
 }
 
 @article{BorchersYngvason:2000,
         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.},
         archiveprefix = {arXiv},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and J. Yngvason},
         eprint = {math-ph/0012020},
         localfile = {2001 - Borchers, Yngvason - On the PCT--Theorem in the Theory of Local Observables.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0012020\\;\%\%},
         title = {{On the PCT-theorem in the theory of local observables}},
         year = {2000}
 }
 
 @inproceedings{BuchholzSummers:2008,
         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.},
         author = {D. Buchholz and S. J. Summers},
         booktitle = {{Quantum Field Theory and Beyond: Essays in Honor of Wolfhart Zimmermann}},
         druck = {Booklet 22.07.08},
         editor = {E. Seiler and K. Sibold},
         keywords = {Mathematical Physics (math-ph); kw:NC-Wick; kw:warping},
         localfile = {2008 - Buchholz, Summers - Warped Convolutions: A Novel Tool in the Construction of Quantum Field Theories.pdf},
         pages = {107--121},
         pdf = {http://arxiv.org/pdf/0806.0349},
         publisher = {World Scientific},
         title = {{Warped Convolutions: A Novel Tool in the Construction of Quantum Field Theories}},
         url = {http://arxiv.org/abs/0806.0349},
         v1descr = {Mon, 2 Jun 2008 18:28:12 GMT (17kb)},
         year = {2008}
 }
 
 @article{CareyPhillipsRennie:2007,
         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.},
         author = {A. L. Carey and J. Phillips and A. Rennie},
         journal = {Preprint},
         keywords = {Operator Algebras (math.OA)},
         localfile = {2007 - Carey, Phillips, Rennie - Semifinite spectral triples associated with graph Cstar-algebras.pdf},
         month = jul,
         pdf = {http://arxiv.org/pdf/0707.3853},
         title = {{Semifinite Spectral Triples associated with Graph C*-Algebras}},
         url = {http://arxiv.org/abs/0707.3853},
         v1descr = {Thu, 26 Jul 2007 02:41:55 GMT (26kb)},
         year = {2007}
 }
 
 @article{GrosseVignesTourneret:2008,
         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.},
         author = {H. Grosse and F. Vignes-Tourneret},
         journal = {Preprint},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2008 - Grosse, Vignes-Tourneret - Minimalist translation-invariant non-commutative scalar field theory.pdf},
         pdf = {http://arxiv.org/pdf/0803.1035},
         title = {{Minimalist translation-invariant non-commutative scalar field theory}},
         url = {http://arxiv.org/abs/0803.1035},
         v1descr = {Fri, 7 Mar 2008 09:21:53 GMT (74kb,D)},
         volume = {arXiv:0803.1035},
         year = {2008}
 }
 
 @article{GurauMagnenRivasseauTanasa:2008,
         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.},
         author = {R. Gurau and J. Magnen and V. Rivasseau and A. Tanasa},
         journal = {Commun. Math. Phys.},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         number = {LPT ORSAY 08-23},
         pages = {275--290},
         pdf = {http://arxiv.org/pdf/0802.0791},
         title = {{A translation-invariant renormalizable non-commutative scalar model}},
         url = {http://arxiv.org/abs/0802.0791},
         v1descr = {Wed, 6 Feb 2008 13:37:22 GMT (47kb)},
         volume = {287},
         year = {2009}
 }
 
 @article{Mund:2008-1,
         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.},
         author = {J. Mund},
         journal = {Annales Henri Poincare},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         pages = {19--34},
         pdf = {http://arxiv.org/pdf/0806.1940},
         title = {{Borchers' Commutation Relations for Sectors with Braid Group Statistics in Low Dimensions}},
         url = {http://arxiv.org/abs/0806.1940},
         v1descr = {Wed, 11 Jun 2008 19:31:17 GMT (16kb)},
         v1url = {http://www.arxiv.org/abs/0806.1940v1},
         v2descr = {Thu, 12 Jun 2008 10:42:36 GMT (18kb)},
         v2url = {http://www.arxiv.org/abs/0806.1940v2},
         v3descr = {Thu, 10 Jul 2008 14:06:16 GMT (18kb)},
         volume = {10},
         year = {2009}
 }
 
 @article{Soloviev:2008,
         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.},
         archiveprefix = {arXiv},
         author = {M. A. Soloviev},
         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.},
         doi = {10.1103/PhysRevD.77.125013},
         eprint = {0802.0997},
         journal = {Phys. Rev.},
         keywords = {kw:NC-Wick},
         localfile = {2008 - Soloviev - On the failure of microcausality in noncommutative field theories.pdf},
         pages = {125013},
         primaryclass = {hep-th},
         slaccitation = {\%\%CITATION = 0802.0997\\;\%\%},
         title = {{On the failure of microcausality in noncommutative field theories}},
         url = {http://arxiv.org/abs/0802.0997},
         volume = {D77},
         year = {2008}
 }
 
 @article{ChaichianMnatsakanovaTureanuVernov:2007,
         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.},
         author = {M. Chaichian and M. Mnatsakanova and A. Tureanu and Yu. Vernov},
         journal = {JHEP},
         keywords = {High Energy Physics - Theory (hep-th)},
         number = {HIP-2007-31/TH},
         pages = {125},
         pdf = {http://arxiv.org/pdf/0706.1712},
         title = {{Test Functions Space in Noncommutative Quantum Field Theory}},
         url = {http://arxiv.org/abs/0706.1712},
         v1descr = {Tue, 12 Jun 2007 14:54:38 GMT (10kb)},
         v1url = {http://www.arxiv.org/abs/0706.1712v1},
         v2descr = {Wed, 16 Apr 2008 12:59:25 GMT (11kb)},
         v2url = {http://www.arxiv.org/abs/0706.1712v2},
         v3descr = {Sat, 26 Jul 2008 14:59:00 GMT (11kb)},
         volume = {0809},
         year = {2008}
 }
 
 @article{DoplicherFredenhagenRoberts:1994,
         author = {S. Doplicher and K. Fredenhagen and J. E. Roberts},
         doi = {10.1016/0370-2693(94)90940-7},
         journal = {Phys. Lett.},
         localfile = {1994 - Doplicher, Fredenhagen, Roberts - Space-time quantization induced by classical gravity.pdf},
         pages = {39--44},
         slaccitation = {\%\%CITATION = PHLTA,B331,39\\;\%\%},
         title = {{Space-time quantization induced by classical gravity}},
         volume = {B331},
         year = {1994}
 }
 
 @book{BogolubovLogunovTodorov:1975,
         author = {N. N. Bogolubov and A. A. Logunov and I. T. Todorov},
         localfile = {http://theory.djvu},
         publisher = {W. A. Benjamin, Inc.},
         title = {{Introduction to Axiomatic Quantum Field Theory}},
         year = {1975}
 }
 
 @article{AkoforBalachandranJoseph:2008,
         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.},
         author = {E. Akofor and A. P. Balachandran and A. Joseph},
         journal = {Int.J.Mod.Phys. A},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA)},
         month = jun,
         pages = {1637--167},
         pdf = {http://arxiv.org/pdf/0803.4351},
         title = {{Quantum Fields on the Groenewold-Moyal Plane}},
         url = {http://arxiv.org/abs/0803.4351},
         v1descr = {Sun, 30 Mar 2008 21:52:15 GMT (131kb)},
         v1url = {http://www.arxiv.org/abs/0803.4351v1},
         v2descr = {Tue, 24 Jun 2008 18:41:23 GMT (473kb)},
         volume = {23},
         year = {2008}
 }
 
 @article{AkoforBalachandranJoJoseph:2007,
         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.},
         author = {E. Akofor and A. P. Balachandran and S. G. Jo and A. Joseph},
         journal = {JHEP},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA)},
         localfile = {2007 - Akofor, Balachandran, Jo, Joseph - Quantum Fields on the Groenwald-Moyal Plane: C, P, T and CPT.pdf},
         number = {045},
         pdf = {http://arxiv.org/pdf/0706.1259},
         title = {{Quantum Fields on the Groenewold-Moyal Plane: C, P, T and CPT}},
         url = {http://arxiv.org/abs/0706.1259},
         v1descr = {Fri, 8 Jun 2007 21:27:32 GMT (62kb)},
         v1url = {http://www.arxiv.org/abs/0706.1259v1},
         v2descr = {Tue, 19 Jun 2007 14:43:18 GMT (63kb)},
         v2url = {http://www.arxiv.org/abs/0706.1259v2},
         v3descr = {Tue, 24 Jul 2007 15:31:07 GMT (63kb)},
         v3url = {http://www.arxiv.org/abs/0706.1259v3},
         v4descr = {Thu, 26 Jul 2007 16:08:47 GMT (63kb)},
         v4url = {http://www.arxiv.org/abs/0706.1259v4},
         v5descr = {Thu, 4 Oct 2007 06:37:30 GMT (63kb)},
         volume = {08},
         year = {2007}
 }
 
 @article{AschieriJurcoSchuppWess:2003,
         archiveprefix = {arXiv},
         author = {P. Aschieri and B. Jurco and P. Schupp and J. Wess},
         doi = {10.1016/S0550-3213(02)00937-9},
         eprint = {hep-th/0205214},
         journal = {Nucl. Phys.},
         localfile = {2002 - Aschieri, Jurco, Schupp, Wess - Noncommutative GUTs, standard model and C,P,T..pdf},
         pages = {45--70},
         slaccitation = {\%\%CITATION = HEP-TH/0205214\\;\%\%},
         title = {{Non-commutative GUTs, standard model and C, P, T}},
         volume = {B651},
         year = {2003}
 }
 
 @article{Soloviev:2006,
         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.},
         author = {M. A. Soloviev},
         druck = {Booklet 25.07.08},
         journal = {Theor.Math.Phys.},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2006 - Soloviev - Axiomatic formulations of nonlocal and noncommutative field theories.pdf},
         month = may,
         number = {FIAN/TD/7-06},
         pages = {257--269},
         pdf = {http://arxiv.org/pdf/hep-th/0605249},
         title = {{Axiomatic formulations of nonlocal and noncommutative field theories}},
         url = {http://arxiv.org/abs/hep-th/0605249},
         v1descr = {Thu, 25 May 2006 11:48:19 GMT (14kb)},
         volume = {147},
         year = {2006}
 }
 
 @article{ChuFurutaInami:2006,
         archiveprefix = {arXiv},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{C.-S.}}}}}}}}}}}}}}}}}}}}}}}}} Chu and K. Furuta and T. Inami},
         eprint = {hep-th/0502012},
         journal = {Int. J. Mod. Phys.},
         localfile = {2006 - Chu, Furuta, Inami - Locality, Causality and Noncommutative Geometry.pdf},
         pages = {67--82},
         slaccitation = {\%\%CITATION = HEP-TH/0502012\\;\%\%},
         title = {{Locality, causality and noncommutative geometry}},
         volume = {A21},
         year = {2006}
 }
 
 @article{FrancoPolito:2005,
         archiveprefix = {arXiv},
         author = {D. H. T. Franco and C. M. M. Polito},
         eprint = {hep-th/0403028},
         journal = {J. Math. Phys.},
         localfile = {2004 - Franco , Polito - A New Derivation of the CPT and Spin-Statistics Theorems in Non-Commutative Field Theories.pdf},
         pages = {083503},
         slaccitation = {\%\%CITATION = HEP-TH/0403028\\;\%\%},
         title = {{A new derivation of the CPT and spin-statistics theorems in non-commutative field theories}},
         volume = {46},
         year = {2005}
 }
 
 @article{GrosseWulkenhaar:2004,
         archiveprefix = {arXiv},
         author = {H. Grosse and R. Wulkenhaar},
         doi = {10.1140/epjc},
         eprint = {hep-th/0402093},
         journal = {Eur. Phys. J.},
         keywords = {NCQFT},
         localfile = {2004 - Grosse, Wulkenhaar - The beta-function in duality-covariant noncommutative phi^4-theory.pdf},
         pages = {277--282},
         slaccitation = {\%\%CITATION = HEP-TH/0402093\\;\%\%},
         title = {{The beta-function in duality-covariant noncommutative phi**4 theory}},
         volume = {C35},
         year = {2004}
 }
 
 @article{DisertoriRivasseau:2007,
         archiveprefix = {arXiv},
         author = {M. Disertori and V. Rivasseau},
         doi = {10.1140/epjc},
         eprint = {hep-th/0610224},
         journal = {Eur. Phys. J.},
         localfile = {2007 - Disertori, Rivasseau - Two and Three Loops Beta Function of Non Commutative Phi^4_4 Theory.pdf},
         pages = {661--671},
         slaccitation = {\%\%CITATION = HEP-TH/0610224\\;\%\%},
         title = {{Two and three loops beta function of non commutative phi(4)**4 theory}},
         volume = {C50},
         year = {2007}
 }
 
 @article{DisertoriGurauMagnenRivasseau:2007,
         archiveprefix = {arXiv},
         author = {M. Disertori and R. Gurau and J. Magnen and V. Rivasseau},
         doi = {10.1016/j.physletb.2007.04.007},
         eprint = {hep-th/0612251},
         journal = {Phys. Lett.},
         localfile = {2007 - Disertori, Gurau, Magnen, Rivasseau - Vanishing of Beta Function of Non Commutative Phi^4_4 Theory to all orders.pdf},
         pages = {95--102},
         slaccitation = {\%\%CITATION = HEP-TH/0612251\\;\%\%},
         title = {{Vanishing of beta function of non commutative phi(4)**4 theory to all orders}},
         volume = {B649},
         year = {2007}
 }
 
 @article{Yngvason:1984,
         author = {J. Yngvason},
         doi = {10.2977/prims},
         journal = {Publ. RIMS, Kyoto University},
         keywords = {kw:NC-Wick},
         localfile = {1984 - Yngvason - On the Locality Ideal in the Algebra of Test Functions for Quantum Fields.pdf},
         number = {20},
         pages = {1063--1081},
         title = {{On the Locality Ideal in the Algebra of Test Functions for Quantum Fields}},
         year = {1984}
 }
 
 @article{LassnerUhlmann:1968,
         author = {G. Lassner and A. Uhlmann},
         journal = {Commun. Math. Phys.},
         localfile = {1968 - Lassner, Uhlmann - On positive functionals on algebras of test functions for quantum fields.pdf},
         pages = {152--159},
         title = {{On positive functionals on algebras of test functions for quantum fields}},
         volume = {7},
         year = {1968}
 }
 
 @article{HollandsWald:2008,
         archiveprefix = {arXiv},
         author = {S. Hollands and R. M. Wald},
         eprint = {0803.2003},
         journal = {Preprint},
         localfile = {2008 - Hollands, Wald - Axiomatic quantum field theory in curved spacetime.pdf},
         primaryclass = {gr-qc},
         slaccitation = {\%\%CITATION = 0803.2003\\;\%\%},
         title = {{Axiomatic quantum field theory in curved spacetime}},
         year = {2008}
 }
 
 @article{LeylandsRobertsTestard:1978,
         author = {P. Leylands and J. E. Roberts and D. Testard},
         journal = {Preprint},
         localfile = {1978 - Leyland, Roberts, Testard - Duality for Quantum Free Fields.pdf},
         title = {{Duality for Quantum Free Fields}},
         year = {1978}
 }
 
 @article{Buchholz:2008,
         abstract = {Buchholz' Vortrag anl\"{a}{\ss}lich der Verleihung der Max-Planck Medaille.},
         author = {D. Buchholz},
         journal = {Physik Journal},
         localfile = {2008 - Buchholz - Ein alternativer Zugang zur Teilchenphysik.pdf},
         title = {{Quantenfeldtheorie ohne Felder}},
         year = {2008}
 }
 
 @article{GrosseLechner:2008,
         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.},
         author = {H. Grosse and G. Lechner},
         doi = {10.1088/1126-6708},
         journal = {JHEP},
         keywords = {kw:NC-Wick; kw:warping},
         localfile = {2008 - Grosse, Lechner - Noncommutative Deformations of Wightman Quantum Field Theories.pdf},
         pages = {131},
         title = {{Noncommutative Deformations of Wightman Quantum Field Theories}},
         url = {http://arxiv.org/abs/0808.3459},
         volume = {09},
         x-color = {#199bff},
         year = {2008}
 }
 
 @techreport{GrosseVignesTourneret:2008-1,
         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.},
         author = {H. Grosse and F. Vignes-Tourneret},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2008 - Grosse, Vignes-Tourneret - Quantum field theory on the degenerate Moyal space.pdf},
         month = oct,
         number = {UWThPh-2008-05},
         pdf = {http://arxiv.org/pdf/0803.1035},
         title = {{Quantum field theory on the degenerate Moyal space}},
         url = {http://arxiv.org/abs/0803.1035},
         v1descr = {Fri, 7 Mar 2008 09:21:53 GMT (74kb,D)},
         v1url = {http://www.arxiv.org/abs/0803.1035v1},
         v2descr = {Tue, 7 Oct 2008 13:16:36 GMT (82kb,D)},
         year = {2008}
 }
 
 @article{FischerSzabo:2008,
         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.},
         author = {A. Fischer and R. J. Szabo},
         doi = {10.1088/1126-6708},
         journal = {JHEP},
         keywords = {High Energy Physics - Theory (hep-th); kw:NC-Wick},
         localfile = {2008 - Fischer, Szabo - Duality covariant quantum field theory on noncommutative Minkowski space.pdf},
         pages = {031},
         pdf = {http://arxiv.org/pdf/0810.1195},
         title = {{Duality covariant quantum field theory on noncommutative Minkowski space}},
         url = {http://arxiv.org/abs/0810.1195},
         v1descr = {Tue, 7 Oct 2008 14:01:33 GMT (35kb)},
         v1url = {http://www.arxiv.org/abs/0810.1195v1},
         v2descr = {Mon, 3 Nov 2008 11:02:34 GMT (35kb)},
         v2url = {http://www.arxiv.org/abs/0810.1195v2},
         v3descr = {Tue, 10 Feb 2009 10:24:39 GMT (35kb)},
         volume = {0902},
         year = {2009}
 }
 
 @article{BuchholzHaag:1999,
         abstract = {We discuss the status and some perspectives of relativistic quantum physics.},
         author = {D. Buchholz and R. Haag},
         journal = {J.Math.Phys. 41 (2000) 3674-3697},
         keywords = {High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)},
         localfile = {1999 - Buchholz, Haag - The Quest for Understanding in Relativistic Quantum Physics.pdf},
         month = nov,
         pdf = {http://arxiv.org/pdf/hep-th/9910243},
         title = {{The Quest for Understanding in Relativistic Quantum Physics}},
         url = {http://arxiv.org/abs/hep-th/9910243},
         v1descr = {Fri, 29 Oct 1999 15:26:52 GMT (37kb)},
         v1url = {http://www.arxiv.org/abs/hep-th/9910243v1},
         v2descr = {Fri, 26 Nov 1999 14:04:49 GMT (38kb)},
         year = {1999}
 }
 
 @article{Symanzik:1966,
         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.},
         author = {K. Symanzik},
         journal = {J. Math. Phys.},
         keywords = {Euclidian QFT},
         localfile = {1966 - Symanzik - Euclidean Quantum Field Theory. I. Equations for a Scalar Model.pdf},
         pages = {510--525},
         title = {{Euclidean Quantum Field Theory. I. Equations for a Scalar Model}},
         volume = {7},
         year = {1966}
 }
 
 @article{Schlingemann:1999,
         author = {D. Schlingemann},
         journal = {Preprint},
         localfile = {1999 - Schlingemann - Short-distance analysis for algebraic euclidean field theory.pdf},
         title = {{Short-distance analysis for algebraic euclidean field theory}},
         year = {1999}
 }
 
 @article{Schlingemann:1999-1,
         author = {D. Schlingemann},
         journal = {Rev. Math. Phys.},
         keywords = {kw:NC-Wick},
         localfile = {1999 - Schlingemann - From Euclidean Field Theory to Quantum Field Theory.pdf},
         pages = {1151--1178},
         title = {{From Euclidean Field Theory to Quantum Field Theory}},
         url = {http://arxiv.org/abs/hep-th/9802035},
         volume = {11},
         year = {1999}
 }
 
 @misc{RedeiSummers:2008,
         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.},
         author = {M. Redei and S. J. Summers},
         journal = {Preprint},
         keywords = {Mathematical Physics (math-ph); Quantum Physics (quant-ph)},
         localfile = {2008 - Redei, Summers - When are quantum systems operationally independent.pdf},
         month = oct,
         pdf = {http://arxiv.org/pdf/0810.5294},
         title = {{When are quantum systems operationally independent?}},
         url = {http://arxiv.org/abs/0810.5294},
         v1descr = {Wed, 29 Oct 2008 14:49:42 GMT (13kb)},
         year = {2008}
 }
 
 @article{BorchersYngvason:1998,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and J. Yngvason},
         journal = {J.Math.Phys. 40 (1999) 601-624},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {1999 - Borchers, Yngvason - Modular groups of quantum fields in thermal states.pdf},
         month = may,
         number = {Erwin Schroedinger Institute preprint Nr. ESI-551},
         pdf = {http://arxiv.org/pdf/math-ph/9805013},
         title = {{Modular Groups of Quantum Fields in Thermal States}},
         url = {http://arxiv.org/abs/math-ph/9805013},
         v1descr = {Fri, 15 May 1998 10:59:22 GMT (37kb)},
         year = {1998}
 }
 
 @article{ArinshteinFateevZamolodchikov:1979,
         author = {A. E. Arinshtein and V. A. Fateev and A. B. Zamolodchikov},
         doi = {10.1016/0370-2693(79)90561-6},
         journal = {Phys. Lett.},
         pages = {389--392},
         slaccitation = {\%\%CITATION = PHLTA,B87,389\\;\%\%},
         title = {{Quantum S-Matrix of the (1+1)-Dimensional Toda Chain}},
         volume = {B87},
         year = {1979}
 }
 
 @techreport{FendleySaleur:1993,
         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.},
         author = {P. Fendley and H. Saleur},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {1993 - Fendley, Saleur - Massless integrable quantum field theories and massless scattering in 1+1 dimensions.pdf},
         month = oct,
         number = {USC-93-022},
         pdf = {http://arxiv.org/pdf/hep-th/9310058},
         title = {{Massless integrable quantum field theories and massless scattering in 1+1 dimensions}},
         url = {http://arxiv.org/abs/hep-th/9310058},
         v1descr = {Mon, 11 Oct 1993 20:08:37 GMT (30kb)},
         year = {1993}
 }
 
 @article{FredenhagenRehrenSchroer:1992,
         author = {K. Fredenhagen and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren and B. Schroer},
         journal = {Rev. Math. Phys.},
         pages = {113--157},
         slaccitation = {\%\%CITATION = RMPHE,SI1,113\\;\%\%},
         title = {{Superselection sectors with braid group statistics and exchange algebras. 2. Geometric aspects and conformal covariance}},
         volume = {SI1},
         year = {1992}
 }
 
 @article{FredenhagenJr:1996,
         author = {K. Fredenhagen and M. J{\"{o}}r{\ss}},
         doi = {10.1007/BF02099249},
         journal = {Commun. Math. Phys.},
         localfile = {1996 - Fredenhagen, J\"{o}r{\ss} - Conformal Haag-Kastler nets, pointlike localized fields and the existence of operator product expansions.pdf},
         pages = {541--554},
         slaccitation = {\%\%CITATION = CMPHA,176,541\\;\%\%},
         title = {{Conformal Haag-Kastler nets, point-like localized fields and the existence of operator product expansions}},
         volume = {176},
         year = {1996}
 }
 
 @article{FredenhagenSchomerus:2001,
         archiveprefix = {arXiv},
         author = {S. Fredenhagen and V. Schomerus},
         eprint = {hep-th/0104043},
         slaccitation = {\%\%CITATION = HEP-TH/0104043\\;\%\%},
         title = {{Brane dynamics in CFT backgrounds}},
         year = {2001}
 }
 
 @article{FredenhagenSchomerus:2003,
         archiveprefix = {arXiv},
         author = {S. Fredenhagen and V. Schomerus},
         doi = {10.1103/PhysRevD.67.085001},
         eprint = {hep-th/0205011},
         journal = {Phys. Rev.},
         pages = {085001},
         slaccitation = {\%\%CITATION = HEP-TH/0205011\\;\%\%},
         title = {{On boundary RG-flows in coset conformal field theories}},
         volume = {D67},
         year = {2003}
 }
 
 @article{DAntoniFredenhagenKoster:2004,
         archiveprefix = {arXiv},
         author = {C. D'Antoni and K. Fredenhagen and S. Koster},
         doi = {10.1023/B:MATH.0000035040.57943.7e},
         eprint = {math-ph/0312017},
         journal = {Lett. Math. Phys.},
         pages = {239--247},
         slaccitation = {\%\%CITATION = MATH-PH/0312017\\;\%\%},
         title = {{Implementation of conformal covariance by diffeomorphism symmetry}},
         volume = {67},
         year = {2004}
 }
 
 @article{FredenhagenGaberdielKeller:2007,
         archiveprefix = {arXiv},
         author = {S. Fredenhagen and M. R. Gaberdiel and C. A. Keller},
         doi = {10.1088/1751-8113},
         eprint = {0707.2511},
         journal = {J. Phys.},
         pages = {13685--13710},
         primaryclass = {hep-th},
         slaccitation = {\%\%CITATION = 0707.2511\\;\%\%},
         title = {{Symmetries of perturbed conformal field theories}},
         volume = {A40},
         year = {2007}
 }
 
 @techreport{Kasprzak:2008,
         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.},
         author = {P. Kasprzak},
         keywords = {Operator Algebras (math.OA); Quantum Algebra (math.QA)},
         localfile = {2008 - Kasprzak - Rieffel Deformations via Crossed Products.pdf},
         month = jan,
         number = {KBN: 115/E-343/SPB/6.PR UE/DIE50/2005-2008},
         pdf = {http://arxiv.org/pdf/math/0606333},
         title = {{Rieffel Deformation via crossed products}},
         url = {http://arxiv.org/abs/math/0606333},
         v10descr = {Mon, 16 Jul 2007 09:57:45 GMT (34kb)},
         v10url = {http://www.arxiv.org/abs/math/0606333v10},
         v11descr = {Fri, 30 Nov 2007 09:05:28 GMT (35kb)},
         v11url = {http://www.arxiv.org/abs/math/0606333v11},
         v12descr = {Fri, 4 Jan 2008 12:51:58 GMT (33kb)},
         v1descr = {Wed, 14 Jun 2006 10:49:53 GMT (28kb)},
         v1url = {http://www.arxiv.org/abs/math/0606333v1},
         v2descr = {Tue, 20 Jun 2006 13:49:00 GMT (30kb)},
         v2url = {http://www.arxiv.org/abs/math/0606333v2},
         v3descr = {Wed, 21 Jun 2006 16:31:10 GMT (31kb)},
         v3url = {http://www.arxiv.org/abs/math/0606333v3},
         v4descr = {Fri, 25 Aug 2006 14:53:21 GMT (31kb)},
         v4url = {http://www.arxiv.org/abs/math/0606333v4},
         v5descr = {Wed, 30 Aug 2006 16:29:47 GMT (31kb)},
         v5url = {http://www.arxiv.org/abs/math/0606333v5},
         v6descr = {Tue, 7 Nov 2006 13:00:38 GMT (31kb)},
         v6url = {http://www.arxiv.org/abs/math/0606333v6},
         v7descr = {Fri, 24 Nov 2006 18:01:18 GMT (33kb)},
         v7url = {http://www.arxiv.org/abs/math/0606333v7},
         v8descr = {Mon, 27 Nov 2006 12:28:12 GMT (33kb)},
         v8url = {http://www.arxiv.org/abs/math/0606333v8},
         v9descr = {Tue, 28 Nov 2006 00:08:07 GMT (33kb)},
         v9url = {http://www.arxiv.org/abs/math/0606333v9},
         year = {2008}
 }
 
 @article{Rieffel:1990,
         author = {M. A. Rieffel},
         journal = {Proc. Symp. Pure Math.},
         localfile = {1990 - Rieffel - Deformation Quantization and Operator Algebras.pdf},
         number = {51},
         pages = {411--423},
         title = {{Deformation Quantization and Operator Algebras}},
         year = {1990}
 }
 
 @techreport{Waldmann:2004,
         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.},
         author = {S. Waldmann},
         keywords = {Mathematical Physics (math-ph); Quantum Algebra (math.QA)},
         localfile = {2004 - Waldmann - States and representations in deformation quantization.pdf},
         month = aug,
         number = {FR-THEP 2004/15},
         pdf = {http://arxiv.org/pdf/math/0408217},
         title = {{States and representations in deformation quantization}},
         url = {http://arxiv.org/abs/math/0408217},
         v1descr = {Tue, 17 Aug 2004 08:30:03 GMT (70kb)},
         year = {2004}
 }
 
 @article{HellerNeumaierWaldmann:2006,
         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.},
         author = {J. G. Heller and N. Neumaier and S. Waldmann},
         journal = {Lett. Math. Phys.},
         keywords = {Mathematical Physics (math-ph); Quantum Algebra (math.QA); kw:local-ncqft},
         localfile = {2006 - Heller, Neumaier, Waldmann - A C-Algebraic Model for Locally Noncommutative Spacetimes.pdf},
         pages = {257--272},
         pdf = {http://arxiv.org/pdf/math/0609850},
         title = {{A C*-Algebraic Model for Locally Noncommutative Spacetimes}},
         url = {http://arxiv.org/abs/math/0609850},
         v1descr = {Fri, 29 Sep 2006 18:56:33 GMT (17kb)},
         volume = {80},
         year = {2007}
 }
 
 @techreport{Waldmann:1999,
         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.},
         author = {S. Waldmann},
         keywords = {Mathematical Physics (math-ph); Quantum Algebra (math.QA); Symplectic Geometry (math.SG)},
         localfile = {1999 - Waldmann - Locality in GNS Representations of Deformation Quantization.pdf},
         month = mar,
         number = {FR-THEP-99/2},
         pdf = {http://arxiv.org/pdf/math/9903053},
         title = {{Locality in GNS Representations of Deformation Quantization}},
         url = {http://arxiv.org/abs/math/9903053},
         v1descr = {Tue, 9 Mar 1999 21:46:42 GMT (35kb)},
         year = {1999}
 }
 
 @misc{Lled:2009,
         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.},
         author = {F. Lled{\'{o}}},
         keywords = {Mathematical Physics (math-ph); Operator Algebras (math.OA)},
         localfile = {2009 - Lledo - Modular Theory by Example.pdf},
         month = jan,
         pdf = {http://arxiv.org/pdf/0901.1004},
         title = {{Modular Theory by example}},
         url = {http://arxiv.org/abs/0901.1004},
         v1descr = {Thu, 8 Jan 2009 10:10:53 GMT (27kb)},
         year = {2009}
 }
 
 @misc{BostelmannDAntoniMorsella:2008,
         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.},
         author = {H. Bostelmann and C. D'Antoni and G. Morsella},
         keywords = {Mathematical Physics (math-ph); Algebraic Quantum Field Theory},
         localfile = {2008 - Bostelmann, D'Antoni, Morsella - On dilation symmetries arising from scaling limits.pdf},
         month = dec,
         pdf = {http://arxiv.org/pdf/0812.4762},
         title = {{On dilation symmetries arising from scaling limits}},
         url = {http://arxiv.org/abs/0812.4762},
         v1descr = {Sat, 27 Dec 2008 18:52:22 GMT (47kb)},
         year = {2008}
 }
 
 @misc{BostelmannFewster:2008,
         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.},
         author = {H. Bostelmann and C. J. Fewster},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {2008 - Bostelmann, Fewster - Quantum Inequalities from Operator Product Expansions.pdf},
         month = dec,
         pdf = {http://arxiv.org/pdf/0812.4760},
         title = {{Quantum Inequalities from Operator Product Expansions}},
         url = {http://arxiv.org/abs/0812.4760},
         v1descr = {Sat, 27 Dec 2008 19:15:02 GMT (43kb)},
         year = {2008}
 }
 
 @article{KaschekNeumaierWaldmann:2009,
         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.},
         author = {D. Kaschek and N. Neumaier and S. Waldmann},
         doi = {10.4171/JNCG},
         journal = {J. Noncommutative Geometry},
         keywords = {Astrophysics (astro-ph); kw:local-ncqft; Mathematical Physics (math-ph); Operator Algebras (math.OA)},
         localfile = {2008 - Kaschek, Neumaier, Waldmann - Complete Positivity of Rieffel's Deformation Quantization by Actions of Rd.pdf},
         month = nov,
         pages = {361--375},
         pdf = {http://arxiv.org/pdf/0809.2206},
         title = {{Complete Positivity of Rieffel's Deformation Quantization by Actions of $R^d$}},
         url = {http://arxiv.org/abs/0809.2206},
         v1descr = {Fri, 12 Sep 2008 12:57:53 GMT (15kb)},
         v1url = {http://www.arxiv.org/abs/0809.2206v1},
         v2descr = {Thu, 25 Sep 2008 08:52:24 GMT (15kb)},
         v2url = {http://www.arxiv.org/abs/0809.2206v2},
         v3descr = {Mon, 17 Nov 2008 08:49:27 GMT (16kb)},
         volume = {3},
         year = {2009}
 }
 
 @article{Wyss:1972,
         author = {W. Wyss},
         doi = {10.1007/BF01645693},
         journal = {Commun. Math. Phys.},
         localfile = {1972 - Wyss - The Field algebra and its positive linear functionals.pdf},
         pages = {223--234},
         slaccitation = {\%\%CITATION = CMPHA,27,223\\;\%\%},
         title = {{The field algebra and its positive linear functionals}},
         volume = {27},
         year = {1972}
 }
 
 @article{Florig:1998,
         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.},
         author = {M. Florig},
         doi = {10.1023/A:1007546507392},
         journal = {Lett. Math. Phys.},
         localfile = {1998 - Florig - On Borchers' theorem.pdf},
         pages = {289--293},
         slaccitation = {\%\%CITATION = LMPHD,46,289\\;\%\%},
         title = {{On Borchers' theorem}},
         volume = {46},
         year = {1998}
 }
 
 @article{Piacitelli:2009,
         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''?},
         author = {G. Piacitelli},
         journal = {Preprint},
         localfile = {2009 - Piacitelli - Twisted Covariance vs Weyl Quantisation.pdf},
         title = {{Twisted Covariance vs Weyl Quantisation}},
         year = {2009}
 }
 
 @article{BievreMerkli:2006,
         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.},
         author = {S. De Bievre and M. Merkli},
         journal = {Class.Quant.Grav.23:6525-6542,2006},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {2006 - De Bievre, Merkli - The Unruh effect revisited.pdf},
         month = apr,
         pdf = {http://arxiv.org/pdf/math-ph/0604023},
         title = {{The Unruh effect revisited}},
         url = {http://arxiv.org/abs/math-ph/0604023},
         v1descr = {Tue, 11 Apr 2006 12:50:05 GMT (22kb)},
         year = {2006}
 }
 
 @misc{Summers:2008-2,
         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.},
         author = {S. J. Summers},
         keywords = {Algebraic Quantum Field Theory; Mathematical Physics (math-ph); Operator Algebras (math.OA); Quantum Physics (quant-ph)},
         localfile = {2008 - Summers - Subsystems and Independence in Relativistic Microscopic Physics.pdf},
         month = dec,
         pdf = {http://arxiv.org/pdf/0812.1517},
         title = {{Subsystems and Independence in Relativistic Microscopic Physics}},
         url = {http://arxiv.org/abs/0812.1517},
         v1descr = {Mon, 8 Dec 2008 16:32:42 GMT (22kb)},
         year = {2008}
 }
 
 @phdthesis{Dybalski:2009,
         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.},
         author = {W. Dybalski},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2008 - Dybalski - Spectral Theory of Automorphism Groups and Particle Structures in Quantum Field Theory.pdf},
         month = jan,
         pdf = {http://arxiv.org/pdf/0901.3127},
         school = {G\"{o}ttingen},
         title = {{Spectral Theory of Automorphism Groups and Particle Structures in Quantum Field Theory}},
         url = {http://arxiv.org/abs/0901.3127},
         v1descr = {Tue, 20 Jan 2009 19:46:48 GMT (135kb)},
         year = {2009}
 }
 
 @book{Rudin:1970,
         author = {W. Rudin},
         keywords = {Analysis; Funktionentheorie},
         localfile = {http://analysis.djvu},
         title = {{Real and complex analysis}},
         year = {1970}
 }
 
 @book{KadisonRingrose:1983,
         author = {R. V. Kadison and J. R. Ringrose},
         keywords = {Operatoralgebren; Book},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Kadison, Ringrose - Fundamentals of the Theory of Operator Algebras I - Elementary Theory.pdf},
         title = {{Fundamentals of the Theory of Operator Algebras I - Elementary Theory}},
         year = {1983}
 }
 
 @book{KadisonRingrose:1986,
         author = {R. V. Kadison and J. R. Ringrose},
         keywords = {Operatoralgebren; Book},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Kadison, Ringrose - Fundamentals of the Theory of Operator Algebras II - Advanced Theory.pdf},
         title = {{Fundamentals of the Theory of Operator Algebras II - Advanced Theory}},
         year = {1986}
 }
 
 @book{Landi:2002,
         author = {G. Landi},
         keywords = {Nichtkommutative Geometrie; Book},
         localfile = {/home/gandalf/Physik/Lecture Notes/1997 - Landi - An Introduction to Noncommutative Spaces and their Geometry.pdf},
         title = {{An Introduction to Noncommutative Spaces and their Geometries}},
         year = {2002}
 }
 
 @book{BaezSegalZhou:1992,
         author = {J. Baez and I. E. Segal and Z. Zhou},
         keywords = {Algebraische QFT; Book; Konstruktive QFT},
         localfile = {http://theory.djvu},
         title = {{Introduction to Algebraic and Constructive Quantum Field Theory}},
         year = {1992}
 }
 
 @book{BratteliRobinson:1987,
         author = {O. Bratteli and D. W. Robinson},
         keywords = {Book; Operatoralgebren; Quantenstatistik},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Bratteli, Robinson - Operator Algebras and Quantum Statistical Mechanics. Vol. 1.djvu},
         title = {{Operator Algebras and Quantum Statistical Mechanics I}},
         year = {1987}
 }
 
 @book{BratteliRobinson:1997,
         author = {O. Bratteli and D. W. Robinson},
         keywords = {Book; Operatoralgebren; Quantenstatistik},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Bratteli, Robinson - Operator Algebras and Quantum Statistical Mechanics. Vol. 2.djvu},
         publisher = {Springer},
         title = {{Operator Algebras and Quantum Statistical Mechanics II}},
         year = {1997}
 }
 
 @book{Haag:1996A,
         author = {R. Haag},
         edition = {2},
         keywords = {Algebraische QFT; Book; kw:NC-Wick; QFT},
         localfile = {http://algebras.djvu},
         publisher = {Springer},
         title = {{Local Quantum Physics - Fields, Particles, Algebras}},
         year = {1996}
 }
 
 @book{Jost:1965,
         author = {R. Jost},
         keywords = {Book; QFT; Wightman-QFT},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Jost - General theory of quantized fields (AMS, 1964)(L)(T)(86s).djvu},
         title = {{The General Theory of Quantized Fields}},
         year = {1965}
 }
 
 @phdthesis{Boller:2002,
         author = {S. Boller},
         keywords = {Modular Theory; Operatoralgebren},
         localfile = {2002 - Boller - Spectral Theory of Modular Operators for von Neumann Algebras and Related Inverse Problems.pdf},
         school = {Leipzig},
         title = {{Spectral Theory of Modular Operators for von Neumann Algebras and Related Inverse Problems}},
         year = {2002}
 }
 
 @article{LeitzMartiniWollenberg:2000,
         author = {M. Leitz-Martini and M. Wollenberg},
         journal = {Z. Anal. Anw.},
         keywords = {Algebraische QFT; Operatoralgebren},
         localfile = {2000 - Leitz-Martini, Wollenberg - Notes on Modular Conjugations of von Neumann Factors.pdf},
         number = {19},
         pages = {13--22},
         title = {{Notes on Modular Conjugations of von Neumann Factors}},
         url = {http://www.emis.de/journals/ZAA/1901/2.html},
         year = {2000}
 }
 
 @misc{Piacitelli:2009-1,
         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.},
         author = {G. Piacitelli},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
         localfile = {2009 - Piacitelli - Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model.pdf},
         month = feb,
         pdf = {http://arxiv.org/pdf/0902.0575},
         title = {{Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model}},
         url = {http://arxiv.org/abs/0902.0575},
         v1descr = {Tue, 3 Feb 2009 18:22:47 GMT (27kb)},
         year = {2009}
 }
 
 @book{Takesaki:2001,
         author = {M. Takesaki},
         keywords = {Operatoralgebren},
         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},
         publisher = {Springer},
         title = {{Theory of Operator Algebras I}},
         year = {2001}
 }
 
 @book{Takesaki:2003,
         author = {M. Takesaki},
         keywords = {Operatoralgebren},
         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},
         publisher = {Springer},
         title = {{Theory of Operator Algebras II}},
         year = {2003}
 }
 
 @book{Takesaki:2003-1,
         author = {M. Takesaki},
         keywords = {Operatoralgebren},
         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},
         publisher = {Springer},
         title = {{Theory of Operator Algebras III}},
         year = {2003}
 }
 
 @book{Connes:1990,
         author = {A. Connes},
         keywords = {Nichtkommutative Geometrie},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Connes - Noncommutative Geometry.pdf},
         publisher = {InterEditions Paris},
         title = {{Noncommutative Geometry}},
         year = {1990}
 }
 
 @book{ReedSimon:1972,
         author = {M. Reed and B. Simon},
         keywords = {Functional Analysis},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Reed, Simon - Methods of Modern Mathematical Physics I - Functional Analysis.pdf},
         publisher = {Academic Press},
         title = {{Methods of Modern Mathematical Physics I - Functional Analysis}},
         year = {1972}
 }
 
 @book{ReedSimon:1975,
         author = {M. Reed and B. Simon},
         keywords = {Analysis; Functional Analysis; kw:NC-Wick},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Reed, Simon - Methods of Modern Mathematical Physics II - Fourier Analysis, Self-Adjointness.pdf},
         publisher = {Academic Press},
         title = {{Methods of Modern Mathematical Physics II - Fourier Analysis}},
         year = {1975}
 }
 
 @book{ReedSimon:1979,
         author = {M. Reed and B. Simon},
         keywords = {Analysis; Functional Analysis},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Reed, Simon - Methods of Modern Mathematical Physics III - Scattering Theory.pdf},
         publisher = {Academic Press},
         title = {{Methods of Modern Mathematical Physics III - Scattering Theory}},
         year = {1979}
 }
 
 @book{ReedSimon:1978,
         author = {M. Reed and B. Simon},
         keywords = {Analysis; Functional Analysis},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Reed, Simon - Methods of Modern Mathematical Physics IV - Analysis of Operators.pdf},
         publisher = {Academic Press},
         title = {{Methods of Modern Mathematical Physics IV - Analysis of Operators}},
         year = {1978}
 }
 
 @book{Conway:1978,
         address = {New York, Heidelberg, Berlin},
         author = {J.B. Conway},
         edition = {2},
         keywords = {Analysis; komplexe Analysis},
         localfile = {http://i.djvu},
         publisher = {Springer},
         title = {{Functions of One Complex Variable}},
         year = {1978}
 }
 
 @book{vonNeumann:1968,
         author = {J. {von Neumann}},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Neumann - Mathematische Grundlagen der Quantenmechanik.pdf},
         publisher = {Springer},
         title = {{Mathematische Grundlagen der Quantenmechanik}},
         year = {1968}
 }
 
 @book{Landsman:1998,
         address = {New York, Heidelberg, Berlin},
         author = {N. P. Landsman},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Landsman - Mathematical topics between classical and quantum mechanics.djvu},
         publisher = {Springer},
         title = {{Mathematical Topics Between Classical and Quantum Mechanics}},
         year = {1998}
 }
 
 @article{Uhlmann:1962,
         author = {A. Uhlmann},
         journal = {Wissenschaftliche Zeitschrift der Karl-Marx-Universit\"{a}t Leipzig},
         keywords = {kw:NC-Wick},
         localfile = {1962 - Uhlmann - \"{U}ber die Definition der Quantenfelder nach Wightman und Haag.pdf},
         pages = {213--217},
         title = {{\"{U}ber die Definition der Quantenfelder nach Wightman und Haag}},
         volume = {2},
         year = {1962}
 }
 
 @inproceedings{Borchers:1972,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         booktitle = {{Statistical mechanics and field theory}},
         editor = {R. N. Sen and C. Weil},
         localfile = {1972 - Borchers - Algebraic Aspects of Wightman Field Theory.pdf},
         publisher = {Halsted Press},
         series = {{Lectures given at the 1971 Haifa Summer School}},
         title = {{Algebraic Aspects of Wightman Quantum Field Theory}},
         year = {1972}
 }
 
 @article{BorrisVerch:2008,
         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.},
         archiveprefix = {arXiv},
         author = {M. Borris and R. Verch},
         doi = {10.1007/s00220-009-0905-2},
         eprint = {0812.0786},
         journal = {Commun. Math. Phys.},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Algebra (math.QA); kw:NC-Wick; kw:local-ncqft},
         localfile = {2008 - Borris, Verch - Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering.pdf},
         pages = {399--448},
         pdf = {http://arxiv.org/pdf/0812.0786},
         primaryclass = {math-ph},
         slaccitation = {\%\%CITATION = 0812.0786\\;\%\%},
         title = {{Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering}},
         url = {http://arxiv.org/abs/0812.0786},
         v1descr = {Wed, 3 Dec 2008 19:37:22 GMT (53kb)},
         volume = {293},
         year = {2010}
 }
 
 @book{Rieffel:1992,
         address = {Providence, Rhode Island},
         author = {M. A. Rieffel},
         keywords = {kw:NC-Wick},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Rieffel - Deformation Quantization for Actions of Rd.pdf},
         publisher = {American Mathematical Society},
         series = {{Memoirs of the Amerian Mathematical Society}},
         title = {{Deformation Quantization for Actions of $R^d$}},
         volume = {106},
         year = {1992}
 }
 
 @article{Rehren:1997,
         archiveprefix = {arXiv},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         doi = {10.1023/A:1007368012557},
         eprint = {hep-th/9605156},
         journal = {Lett. Math. Phys.},
         localfile = {1997 - Rehren - Bounded Bose fields.pdf},
         pages = {299--306},
         slaccitation = {\%\%CITATION = HEP-TH/9605156\\;\%\%},
         title = {{Bounded Bose fields}},
         volume = {40},
         year = {1997}
 }
 
 @lecturenotes{Rehren:1997-1,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         localfile = {1997 - Rehren - Konforme Quantenfeldtheorie.pdf; /home/gandalf/Physik/Lecture Notes/1997 - Rehren - Konforme Quantenfeldtheorie.pdf},
         school = {G\"{o}ttingen},
         title = {{Konforme Quantenfeldtheorie}},
         year = {1997}
 }
 
 @book{DiFrancescoMathieuSnchal:1997,
         author = {P. {Di Francesco} and P. Mathieu and D. S{\'{e}}n{\'{e}}chal},
         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},
         publisher = {Springer},
         title = {{Conformal Field Theory}},
         year = {1997}
 }
 
 @article{Bckenhauer:1996,
         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.},
         archiveprefix = {arXiv},
         author = {J. B{\"{o}}ckenhauer},
         doi = {10.1007/BF02101894},
         eprint = {hep-th/9407079},
         journal = {Commun. Math. Phys.},
         localfile = {1996 - B\"{o}ckenhauer - Localized endomorphisms of the chiral Ising model.pdf},
         pages = {265--304},
         pdf = {http://arxiv.org/pdf/hep-th/9407079},
         slaccitation = {\%\%CITATION = HEP-TH/9407079\\;\%\%},
         title = {{Localized endomorphisms of the chiral Ising model}},
         url = {http://arxiv.org/abs/hep-th/9407079},
         volume = {177},
         year = {1996}
 }
 
 @lecturenotes{Fewster:2008,
         author = {C. J. Fewster},
         localfile = {2008 - Fewster - Lectures on quantum field theory in curved spacetime.pdf},
         school = {Leipzig},
         title = {{Lectures on quantum field theory in curved spacetime}},
         year = {2008}
 }
 
 @article{FurlanSotkovTodorov:1989,
         author = {P. Furlan and G. M. Sotkov and I. T. Todorov},
         journal = {Riv. del Nuovo Cimento},
         keywords = {Conformal Quantum Field Theory},
         localfile = {1988 - Furlan, Sotkov, Todorov - Two-dimensional conformal quantum field theory.pdf},
         number = {12},
         pages = {1--202},
         title = {{Two-Dimensional Conformal Quantum Field Theory}},
         volume = {6},
         year = {1989}
 }
 
 @article{LscherMack:1976,
         author = {M. L{\"{u}}scher and G. Mack},
         journal = {unpublished},
         title = {{The energy momentum tensor of critical quantum field theory in 1+1 dimensions}},
         year = {1976}
 }
 
 @article{KawahigashiLongo:2004,
         archiveprefix = {arXiv},
         author = {Y. Kawahigashi and R. Longo},
         eprint = {math-ph/0201015},
         journal = {Ann. Math.},
         keywords = {Algebraic Quantum Field Theory; Conformal Quantum Field Theory},
         localfile = {2004 - Kawahigashi, Longo - Classification of Local Conformal Nets. Case c < 1.pdf},
         pages = {493--522},
         slaccitation = {\%\%CITATION = MATH-PH/0201015\\;\%\%},
         title = {{Classification of local conformal nets: Case c $<$ 1}},
         volume = {160},
         year = {2004}
 }
 
 @article{McCoyTracyWu:1977,
         author = {B. M. McCoy and C. A. Tracy and T. T. Wu},
         doi = {10.1103/PhysRevLett.38.793},
         journal = {Phys. Rev. Lett.},
         localfile = {1977 - McCoy, Tracy, Wu - Two-Dimensional Ising Model as an Exactly Solvable Relativistic Quantum Field Theory: Explicit Formulas for n-Point Functions.pdf},
         pages = {793--796},
         slaccitation = {\%\%CITATION = PRLTA,38,793\\;\%\%},
         title = {{Two-Dimensional Ising Model as an Exactly Solvable Relativistic Quantum Field Theory: Explicit Formulas for n Point Functions}},
         volume = {38},
         year = {1977}
 }
 
 @article{Carpi:1999,
         author = {S. Carpi},
         doi = {10.1023/A:1007517131143},
         journal = {Lett. Math. Phys.},
         localfile = {1999 - Carpi - Classification of Subsystems for the Haag--Kastler Nets Generated by c = 1 Chiral Current Algebras.pdf},
         pages = {353--364},
         slaccitation = {\%\%CITATION = LMPHD,47,353\\;\%\%},
         title = {{Classification of subsystems for the Haag-Kastler nets generated by c = 1 chiral current algebras}},
         volume = {47},
         year = {1999}
 }
 
 @article{Carpi:1998,
         author = {S. Carpi},
         doi = {10.1023/A:1007466420114},
         journal = {Lett. Math. Phys.},
         localfile = {1998 - Carpi - Absence of Subsystems for the Haag--Kastler Net Generated by the Energy-Momentum Tensor in Two-Dimensional Conformal Field Theory.pdf},
         pages = {259--267},
         slaccitation = {\%\%CITATION = LMPHD,45,259\\;\%\%},
         title = {{Absence of subsystems for the Haag-Kastler net generated by the energy-momentum tensor in two-dimensional conformal field theory}},
         volume = {45},
         year = {1998}
 }
 
 @book{Heuser:1995,
         author = {H. Heuser},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Heuser H. Gewoehnliche Differentialgleichungen (Teubner, 1995)(de)(600dpi)(T)(628s)_MCde_.djvu},
         publisher = {Teubner},
         title = {{Gew\"{o}hnliche Differentialgleichungen}},
         year = {1995}
 }
 
 @article{Boller:2000,
         author = {S. Boller},
         journal = {Preprint},
         localfile = {2000 - Boller - Characterization of Cyclic and Separating Vectors and Application to an Inverse Problem in Modular Theory I. Finite Factors.pdf},
         title = {{Characterization of Cyclic and Separating Vectors and Application to an Inverse Problem in Modular Theory I. Finite Factors}},
         year = {2000}
 }
 
 @book{BaumgrtelWollenberg:1992,
         author = {H. Baumg{\"{a}}rtel and M. Wollenberg},
         localfile = {http://algebras.djvu},
         publisher = {Akademie Verlag},
         title = {{Causal Nets of Operator Algebras}},
         year = {1992}
 }
 
 @lecturenotes{Longo:2008,
         author = {R. Longo},
         localfile = {2008 - Longo - Lectures on Conformal Nets - part1.pdf},
         title = {{Lectures on Conformal Nets - Part 1}},
         year = {2008}
 }
 
 @lecturenotes{Longo:2008-1,
         author = {R. Longo},
         localfile = {2008 - Longo - Lectures on Conformal Nets - part2.pdf},
         title = {{Lectures on Conformal Nets - Part 2}},
         year = {2008}
 }
 
 @article{DtschFredenhagen:2001,
         author = {M. D{\"{u}}tsch and K. Fredenhagen},
         journal = {Preprint},
         localfile = {2001 - D\"{u}tsch, Fedenhagen - Perturbative Algebraic Field Theory, and Deformation Quantization.pdf},
         title = {{Perturbative Algebraic Field Theory, and Deformation Quantization}},
         year = {2001}
 }
 
 @mastersthesis{Ritz:2003,
         author = {E. Ritz},
         localfile = {2003 - Ritz - Normalit\"{a}tseigenschaften lokaler Gleichgewichtszust\"{a}nde in der relativistischen Quantenfeldtheorie.pdf},
         title = {{Normalit\"{a}tseigenschaften lokaler Gleichgewichtszust\"{a}nde in der relativistischen Quantenfeldtheorie}},
         year = {2003}
 }
 
 @article{BrunettiFredenhagenKhler:1996,
         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.},
         author = {R. Brunetti and K. Fredenhagen and M. K{\"{o}}hler},
         journal = {Commun. Math. Phys.},
         localfile = {1996 - Brunetti, Fredenhagen, K\"{o}hler - The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes.pdf},
         number = {180},
         pages = {633--652},
         title = {{The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes}},
         year = {1996}
 }
 
 @article{Hollands:2008,
         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.},
         archiveprefix = {arXiv},
         author = {S. Hollands},
         eprint = {0802.2198},
         localfile = {2008 - Hollands - Quantum field theory in terms of consistency conditions I: General framework, and perturbation theory via Hochschild cohomology.pdf},
         pdf = {http://arxiv.org/pdf/0802.2198},
         primaryclass = {hep-th},
         slaccitation = {\%\%CITATION = 0802.2198\\;\%\%},
         title = {{Quantum field theory in terms of consistency conditions I: General framework, and perturbation theory via Hochschild cohomology}},
         url = {http://arxiv.org/abs/0802.2198},
         year = {2008}
 }
 
 @article{Gerstenhaber:1964,
         author = {M. Gerstenhaber},
         journal = {Ann. Math.},
         keywords = {Mathematik},
         localfile = {1964 - Gerstenhaber - On the deformation of rings and algebras.pdf},
         pages = {59--103},
         title = {{On the deformation of rings and algebras}},
         url = {http://www.jstor.org/stable/1970484},
         volume = {79},
         year = {1964}
 }
 
 @misc{NahmKeegan:2009,
         abstract = {Integrable deformations of conformal field theories and the discrete Hirota equations.},
         author = {W. Nahm and S. Keegan},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2009 - Nahm, Keegan - Integrable deformations of CFTs and the discrete Hirota equations.pdf},
         month = may,
         pdf = {http://arxiv.org/pdf/0905.3776},
         title = {{Integrable deformations of CFTs and the discrete Hirota equations}},
         url = {http://arxiv.org/abs/0905.3776},
         v1descr = {Sun, 24 May 2009 16:01:17 GMT (15kb)},
         year = {2009}
 }
 
 @article{GliozziTateo:1995,
         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.},
         archiveprefix = {arXiv},
         author = {F. Gliozzi and R. Tateo},
         doi = {10.1016/0370-2693(95)00125-5},
         eprint = {hep-th/9411203},
         journal = {Phys. Lett.},
         localfile = {1995 - Gliozzi, Tateo - ADE functional dilogarithm identities and integrable models.pdf},
         pages = {84--88},
         pdf = {http://arxiv.org/pdf/hep-th/9411203},
         slaccitation = {\%\%CITATION = HEP-TH/9411203\\;\%\%},
         title = {{ADE functional dilogarithm identities and integrable models}},
         url = {http://arxiv.org/abs/hep-th/9411203},
         volume = {B348},
         year = {1995}
 }
 
 @book{GraciaBondiaVrillyFigueroa:2001,
         address = {Boston, Basel, Berlin},
         author = {J. M. Gracia-Bondia and J. C. V{\'{a}}rilly and H. Figueroa},
         isbn = {0817641246, 9780817641245},
         localfile = {http://geometry.djvu},
         publisher = {Birkh\"{a}user},
         series = {{Birkh\"{a}user Advanced Texts}},
         title = {{Elements of Noncommutative Geometry}},
         year = {2001}
 }
 
 @article{Weaver:1996,
         author = {N. Weaver},
         journal = {J. Oper. Theory},
         localfile = {1996 - Weaver - Deformations of von Neumann algebras.pdf},
         number = {2},
         pages = {223--239},
         title = {{Deformations of von Neumann algebras}},
         volume = {35},
         year = {1996}
 }
 
 @article{Rieffel:1981,
         author = {M. A. Rieffel},
         journal = {Math. Ann.},
         localfile = {1981 - Rieffel - Von Neumann algebras associated with pairs of lattices in Lie groups.pdf},
         pages = {403--418},
         title = {{Von Neumann Algebras Associated with Pairs of Lattices in Lie Groups }},
         volume = {257},
         year = {1981}
 }
 
 @article{Rieffel:1990-1,
         author = {M. A. Rieffel},
         journal = {Cont. Math.},
         localfile = {1990 - Rieffel - Non-commutative tori - a case study of non-commutative differentiable manifolds.pdf},
         pages = {191--121},
         title = {{Non-commutative tori - a case study of non-commutative differentiable manifolds}},
         volume = {105},
         year = {1990}
 }
 
 @misc{Schroer:2009-1,
         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.},
         author = {B. Schroer},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2009 - Schroer - BMS symmetry, holography on null-surfaces and area proportionality of light-slice entropy.pdf},
         month = may,
         pdf = {http://arxiv.org/pdf/0905.4435},
         title = {{BMS symmetry, holography on null-surfaces and area proportionality of light-slice entropy}},
         url = {http://arxiv.org/abs/0905.4435},
         v1descr = {Wed, 27 May 2009 16:31:16 GMT (32kb)},
         year = {2009}
 }
 
 @article{Lester:1984,
         author = {J. A. Lester},
         doi = {10.1063/1.526005},
         journal = {J. Math. Phys.},
         keywords = {cosmological models; lorentz transformations; minkowski space; transformations},
         localfile = {1982 - Lester - The causal automorphism of de Sitter and Einstein cylinder spacetimes.pdf},
         number = {1},
         pages = {113--116},
         title = {{The causal automorphism of de Sitter and Einstein cylinder spacetimes}},
         url = {http://link.aip.org/link/?JMP/25/113/1},
         volume = {25},
         year = {1984}
 }
 
 @article{vanSuijlekom:2004,
         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.},
         author = {W.D. {van Suijlekom}},
         journal = {J.Math.Phys.},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2003 - Suijlekom - The noncommutative Lorentzian cylinder as an isospectral deformation.pdf},
         pages = {537--556},
         pdf = {http://arxiv.org/pdf/math-ph/0310009},
         title = {{The noncommutative Lorentzian cylinder as an isospectral deformation}},
         url = {http://arxiv.org/abs/math-ph/0310009},
         v1descr = {Wed, 8 Oct 2003 15:03:17 GMT (23kb)},
         v1url = {http://www.arxiv.org/abs/math-ph/0310009v1},
         v2descr = {Wed, 15 Oct 2003 13:38:53 GMT (22kb)},
         volume = {45},
         year = {2004}
 }
 
 @article{CoburnXia:1995,
         author = {L.A. Coburn and J. Xia},
         doi = {10.1007/BF02099582},
         journal = {Commun. Math. Phys.},
         localfile = {1995 - Coburn, Xia - Toeplitz Algebras and Rieffel Deformations.pdf},
         number = {1},
         pages = {23--38},
         title = {{Toeplitz algebras and Rieffel deformations.}},
         volume = {168},
         year = {1995}
 }
 
 @misc{BieliavskyMaeda:2002,
         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.},
         author = {P. Bieliavsky and Y. Maeda},
         keywords = {kw:UDF; Mathematical Physics (math-ph); New-Deformations; Quantum Algebra (math.QA); Symplectic Geometry (math.SG)},
         localfile = {2002 - Bieliavsky, Maeda - Convergent Star Product Algebras on 'ax+b'.pdf},
         month = sep,
         pdf = {http://arxiv.org/pdf/math/0209295},
         title = {{Convergent star product algebras on 'ax+b'}},
         url = {http://arxiv.org/abs/math/0209295},
         v1descr = {Mon, 23 Sep 2002 12:25:42 GMT (9kb)},
         year = {2002}
 }
 
 @article{Bieliavsky:2002,
         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.},
         author = {P. Bieliavsky},
         journal = {J. Symplectic Geom.},
         keywords = {Differential Geometry (math.DG); Mathematical Physics (math-ph); Quantum Algebra (math.QA); Symplectic Geometry (math.SG); kw:UDF},
         localfile = {2000 - Bieliavsky - Strict Quantization of Solvable Symmetric Spaces.pdf},
         month = oct,
         number = {2},
         pages = {269--320},
         pdf = {http://arxiv.org/pdf/math/0010004},
         title = {{Strict Quantization of Solvable Symmetric Spaces }},
         url = {http://arxiv.org/abs/math/0010004},
         v1descr = {Sun, 1 Oct 2000 14:46:34 GMT (36kb)},
         volume = {1},
         year = {2002}
 }
 
 @mastersthesis{Heller:2006,
         author = {J. G. Heller},
         keywords = {Deformation Quantization; kw:local-ncqft},
         localfile = {2006 - Heller - Lokal nichtkommutative Raumzeiten und Strikte Deformationsquantisierung - Diplom.pdf},
         note = {Diplomarbeit bei Stefan Waldmann},
         school = {Freiburg},
         title = {{Lokal nichtkommutative Raumzeiten und Strikte Deformationsquantisierung}},
         year = {2006}
 }
 
 @mastersthesis{Kaschek:2008,
         author = {D. Kaschek},
         keywords = {Deformation Quantization},
         localfile = {2008 - Kaschek - Nichtperturbative Deformationstheorie physikalischer Zust\"{a}nde - Diplomarbeit.pdf},
         note = {Diplomarbeit bei Stefan Waldmann},
         title = {{Nichtperturbative Deformationstheorie physikalischer Zust\"{a}nde}},
         year = {2008}
 }
 
 @book{Lance:1995,
         address = {Cambridge},
         author = {E.C. Lance},
         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},
         publisher = {Cambridge University Press},
         title = {{Hilbert C*-Modules. A toolkit for operator algebraists}},
         year = {1995}
 }
 
 @article{FredenhagenHertel:1981,
         author = {K. Fredenhagen and J. Hertel},
         doi = {10.1007/BF01941663},
         journal = {Commun. Math. Phys.},
         localfile = {1981 - Fredenhagen, Hertel - Local algebras of observables and pointlike localized fields.pdf},
         pages = {555},
         slaccitation = {\%\%CITATION = CMPHA,80,555\\;\%\%},
         title = {{LOCAL ALGEBRAS OF OBSERVABLES AND POINT - LIKE LOCALIZED FIELDS}},
         volume = {80},
         year = {1981}
 }
 
 @book{Schiff:1999,
         author = {J. L. Schiff},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Schiff J.L. Laplace Transformation.. Theory and Applications (UTM, Springer,1999)(ISBN 0387986987)(245s)_MCat_.pdf},
         publisher = {Springer},
         title = {{Laplace Transformation - Theory and Applications}},
         year = {1999}
 }
 
 @article{Rivasseau:2009,
         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.},
         author = {V. Rivasseau},
         journal = {Preprint},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {2009 - Rivasseau - Constructive Field Theory in Zero Dimension.pdf},
         month = jun,
         pdf = {http://arxiv.org/pdf/0906.3524},
         title = {{Constructive Field Theory in Zero Dimension}},
         url = {http://arxiv.org/abs/0906.3524},
         v1descr = {Thu, 18 Jun 2009 20:25:47 GMT (26kb,D)},
         year = {2009}
 }
 
 @article{BrosBuchholz:1992,
         author = {J. Bros and D. Buchholz},
         doi = {10.1007/BF01565114},
         journal = {Z. Phys.},
         localfile = {1992 - Bros, Buchholz - Particles and propagators in relativistic thermo field theory.pdf},
         pages = {509--514},
         slaccitation = {\%\%CITATION = ZEPYA,C55,509\\;\%\%},
         title = {{Particles and propagators in relativistic thermo field theory}},
         volume = {C55},
         year = {1992}
 }
 
 @article{BrosBuchholz:1994,
         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.},
         archiveprefix = {arXiv},
         author = {J. Bros and D. Buchholz},
         doi = {10.1016/0550-3213(94)00298-3},
         eprint = {hep-th/9807099},
         journal = {Nucl. Phys.},
         localfile = {1994 - Bros, Buchholz - Towards a Relativistic KMS Condition.pdf},
         pages = {291--318},
         pdf = {http://arxiv.org/pdf/hep-th/9807099},
         slaccitation = {\%\%CITATION = HEP-TH/9807099\\;\%\%},
         title = {{Towards a Relativistic KMS Condition}},
         url = {http://arxiv.org/abs/hep-th/9807099},
         volume = {B429},
         year = {1994}
 }
 
 @article{BrosBuchholz:1995,
         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.},
         archiveprefix = {arXiv},
         author = {J. Bros and D. Buchholz},
         eprint = {hep-th/9511022},
         localfile = {1995 - Bros, Buchholz - Relativistic KMS-condition and Kaellen-Lehmann type representatios of thermal propagators.pdf},
         pdf = {http://arxiv.org/pdf/hep-th/9511022},
         slaccitation = {\%\%CITATION = HEP-TH/9511022\\;\%\%},
         title = {{Relativistic KMS-condition and Kaellen-Lehmann type representatios of thermal propagators}},
         url = {http://arxiv.org/abs/hep-th/9511022},
         year = {1995}
 }
 
 @article{BrosBuchholz:1996,
         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.},
         archiveprefix = {arXiv},
         author = {J. Bros and D. Buchholz},
         eprint = {hep-th/9606046},
         journal = {Ann. Poincare},
         localfile = {1996 - Bros, Buchholz - Axiomatic analyticity properties and representations of particles in thermal quantum field theory.pdf},
         pages = {495--522},
         pdf = {http://arxiv.org/pdf/hep-th/9606046},
         slaccitation = {\%\%CITATION = HEP-TH/9606046\\;\%\%},
         title = {{Axiomatic analyticity properties and representations of particles in thermal quantum field theory}},
         url = {http://arxiv.org/abs/hep-th/9606046},
         volume = {64},
         year = {1996}
 }
 
 @article{BrosBuchholz:1998,
         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.},
         archiveprefix = {arXiv},
         author = {J. Bros and D. Buchholz},
         doi = {10.1103/PhysRevD.58.125012},
         eprint = {hep-th/9608139},
         journal = {Phys. Rev.},
         localfile = {1998 - Bros, Buchholz - The unmasking of thermal Goldstone bosons.pdf},
         pages = {125012},
         pdf = {http://arxiv.org/pdf/hep-th/9608139},
         slaccitation = {\%\%CITATION = HEP-TH/9608139\\;\%\%},
         title = {{The unmasking of thermal Goldstone bosons}},
         url = {http://arxiv.org/abs/hep-th/9608139},
         volume = {D58},
         year = {1998}
 }
 
 @article{BrosBuchholz:2002,
         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.},
         archiveprefix = {arXiv},
         author = {J. Bros and D. Buchholz},
         doi = {10.1016/S0550-3213(02)00059-7},
         eprint = {hep-ph/0109136},
         journal = {Nucl. Phys.},
         localfile = {2002 - Bros, Buchholz - Asymptotic dynamics of thermal quantum fields.pdf},
         pages = {289--310},
         pdf = {http://arxiv.org/pdf/hep-ph/0109136},
         slaccitation = {\%\%CITATION = HEP-PH/0109136\\;\%\%},
         title = {{Asymptotic dynamics of thermal quantum fields}},
         url = {http://arxiv.org/abs/hep-ph/0109136},
         volume = {B627},
         year = {2002}
 }
 
 @article{Jaekel:1998,
         abstract = {The basic ingredients of Tomita-Takesaki modular theory are used to establish cluster estimates. Applications to thermal quantum field theory are discussed.},
         archiveprefix = {arXiv},
         author = {C. D. J{\"{a}}kel},
         eprint = {hep-th/9804017},
         localfile = {1999 - J\"{a}kel - Cluster Estimates for Modular Structures.pdf},
         pdf = {http://arxiv.org/pdf/hep-th/9804017},
         slaccitation = {\%\%CITATION = HEP-TH/9804017\\;\%\%},
         title = {{Cluster estimates for modular structures}},
         url = {http://arxiv.org/abs/hep-th/9804017},
         year = {1998}
 }
 
 @article{Rieffel:1993,
         author = {M. A. Rieffel},
         journal = {Cont. Math.},
         localfile = {1993 - Rieffel - Compact quantum groups associated with toral subgroups.pdf},
         title = {{Compact quantum groups associated with toral subgroups}},
         url = {http://www.math.berkeley.edu/~rieffel/papers/compact.pdf},
         volume = {145},
         year = {1993}
 }
 
 @article{Rieffel:1995,
         author = {M. A. Rieffel},
         journal = {Commun. Math. Phys.},
         localfile = {1995 - Rieffel - Non-compact quantum groups associated with abelian subgroups.pdf},
         pages = {181--201},
         title = {{Non-compact quantum groups associated with abelian subgroups}},
         volume = {171},
         year = {1995}
 }
 
 @article{Rieffel:1974,
         author = {M. A. Rieffel},
         journal = {Adv. Math.},
         localfile = {1974 - Rieffel - Induced Representations of C-Algebras.pdf},
         pages = {176--257},
         title = {{Induced representations of C*-algebras}},
         volume = {13},
         year = {1974}
 }
 
 @article{AkoforBalachandran:2009,
         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.},
         author = {E. Akofor and A. P. Balachandran},
         journal = {Phys. Rev. D},
         keywords = {High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech)},
         localfile = {2009 - Akofor, Balachandran - Finite Temperature Field Theory on the Moyal Plane.pdf},
         number = {SU-4252-885},
         pages = {036008},
         pdf = {http://arxiv.org/pdf/0907.0905},
         title = {{Finite Temperature Field Theory on the Moyal Plane}},
         url = {http://arxiv.org/abs/0907.0905},
         v1descr = {Mon, 6 Jul 2009 17:08:58 GMT (14kb)},
         volume = {80},
         year = {2009}
 }
 
 @article{BertrandBertrand:1998,
         abstract = {The study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f\&gt;0 with linear operators defined on the positive-frequency signals. Full attention is given to its construction which is entirely based on the study of the affine group in a simple and direct way. The correspondence rule is detailed and the associated Wigner function is given. Formulas expressing the basic operation (star-bracket) of the Lie algebra of symbols, which is isomorphic to that of the operators, are obtained. In addition, it is shown that the resulting calculus is covariant under a three-parameter group which contains the affine group as subgroup. This observation is the starting point of an investigation leading to a whole class of symbolic calculi which can be considered as modifications of the original one.},
         archiveprefix = {arXiv},
         author = {J. Bertrand and P. Bertrand},
         doi = {10.1063/1.532484},
         eprint = {physics/9708027},
         journal = {J. Math. Phys.},
         localfile = {1998 - Bertrand, Bertrand - Symbolic calculus on the time-frequency half-plane.pdf},
         pages = {4071--4090},
         pdf = {http://arxiv.org/pdf/physics/9708027},
         slaccitation = {\%\%CITATION = PHYSICS/9708027\\;\%\%},
         title = {{Symbolic calculus on the time frequency half plane}},
         url = {http://arxiv.org/abs/physics/9708027},
         volume = {39},
         year = {1998}
 }
 
 @article{KarowskiKurakSchroer:1979,
         author = {M. Karowski and V. Kurak and B. Schroer},
         doi = {10.1016/0370-2693(79)90523-9},
         journal = {Phys. Lett.},
         localfile = {1978 - Karowski, Kurak, Schroer - Confinement in two-dimensional models with factorization.pdf},
         pages = {200},
         slaccitation = {\%\%CITATION = PHLTA,B81,200\\;\%\%},
         title = {{Confinement in two-dimensional models with factorization}},
         volume = {B81},
         year = {1979}
 }
 
 @mastersthesis{Quella:1999,
         author = {T. Quella},
         keywords = {Form Factor Program},
         localfile = {1999 - Quella - Formfaktoren und Lokalit\"{a}t in integrablen Modellen der Quantenfeldtheorie in 1+1 Dimensionen.pdf},
         school = {FU Berlin},
         title = {{Formfaktoren und Lokalit\"{a}t in integrablen Modellen der Quantenfeldtheorie in 1+1 Dimensionen}},
         year = {1999}
 }
 
 @article{GalluccioLizziVitale:2009,
         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.},
         author = {S. Galluccio and Fedele Lizzi and P. Vitale},
         journal = {JHEP},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2009 - Galluccio, Lizzi, Vitale - Translation Invariance, Commutation Relations and Ultraviolet-Infrared Mixing.pdf},
         month = jul,
         pages = {054},
         pdf = {http://arxiv.org/pdf/0907.3640},
         title = {{Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing}},
         url = {http://arxiv.org/abs/0907.3640},
         v1descr = {Tue, 21 Jul 2009 13:05:42 GMT (27kb)},
         volume = {0909},
         year = {2009}
 }
 
 @book{Arnold:1978,
         author = {V.I. Arnold},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Arnold V.I. Ordinary differential equations (MIT, 1978)(no TOC)(400dpi)(T)(273s).djvu},
         publisher = {MIT},
         title = {{Ordinary differential equations}},
         year = {1978}
 }
 
 @book{Teschl:2004,
         author = {G. Teschl},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Teschl G. Ordinary differential equations (lecture notes, web draft, 2004)(243s).pdf},
         title = {{Ordinary Differential Equations and Dynamical Systems}},
         volume = {Lecture Notes (Web draft)},
         year = {2004}
 }
 
 @book{Chicone:1999,
         author = {C. Chicone},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Chicone C. Ordinary Differential Equations with Applications(TAM 34,Springer,1999)(ISBN 0387985352)(571s)_MCde_.pdf},
         publisher = {Springer},
         series = {{Texts in Applied Mathematics}},
         title = {{Ordinary Differential Equations with Applications}},
         volume = {34},
         year = {1999}
 }
 
 @article{VarillyGraciaBondia:1989,
         author = {J. C. Varilly and J. M. Gracia-Bondia},
         doi = {10.1016/0003-4916(89)90262-5},
         journal = {Annals Phys.},
         localfile = {1989 - Varilly, Gracia-Bondia - The Moyal Representation for Spin.pdf},
         pages = {107--148},
         slaccitation = {\%\%CITATION = APNYA,190,107\\;\%\%},
         title = {{The Moyal representation for spin}},
         volume = {190},
         year = {1989}
 }
 
 @book{Williams:2007,
         address = {Providence, Rhode Island},
         author = {D. P. Williams},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Williams - Crossed products of C-algebras.djvu},
         publisher = {American Mathematical Society},
         title = {{Crossed products of C*-algebras}},
         year = {2007}
 }
 
 @article{Bahns:2009,
         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.},
         author = {D. Bahns},
         journal = {Annales Henri Poincare},
         keywords = {High Energy Physics - Theory (hep-th); kw:NC-Wick; Mathematical Physics (math-ph)},
         localfile = {2009 - Bahns - Schwinger functions in noncommutative quantum field theory.pdf},
         pages = {1273--1283},
         pdf = {http://arxiv.org/pdf/0908.4537},
         title = {{Schwinger functions in noncommutative quantum field theory}},
         url = {http://arxiv.org/abs/0908.4537},
         v1descr = {Mon, 31 Aug 2009 14:02:09 GMT (23kb)},
         volume = {11},
         year = {2010}
 }
 
 @misc{Schroer:2009-2,
         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.},
         author = {B. Schroer},
         keywords = {General Physics (physics.gen-ph)},
         localfile = {2009 - Schroer - Geometry and Localization, a metaphorically related pair.pdf},
         month = jun,
         pdf = {http://arxiv.org/pdf/0906.2067},
         title = {{Geometry and Localization, a metaphorically related pair}},
         url = {http://arxiv.org/abs/0906.2067},
         v1descr = {Thu, 11 Jun 2009 15:08:32 GMT (12kb)},
         v1url = {http://www.arxiv.org/abs/0906.2067v1},
         v2descr = {Mon, 22 Jun 2009 16:40:34 GMT (24kb)},
         v2url = {http://www.arxiv.org/abs/0906.2067v2},
         v3descr = {Tue, 23 Jun 2009 17:19:29 GMT (25kb)},
         year = {2009}
 }
 
 @book{Jaenich:1999,
         author = {K. J{\"{a}}nich},
         edition = {5},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Jaenich K. Funktionentheorie (5ed., Springer, 1999)(de)(L)(T)(ISBN 3540661522)(66s).djvu},
         publisher = {Springer},
         title = {{Funktionentheorie - Eine Einf\"{u}hrung}},
         year = {1999}
 }
 
 @misc{BrunettiFredenhagenHoge:2009,
         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.},
         author = {R. Brunetti and K. Fredenhagen and M. Hoge},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)},
         localfile = {2009 - Brunetti, Fredenhagen, Hoge - Time in quantum physics: From an external parameter to an intrinsic observable.pdf},
         month = sep,
         pdf = {http://arxiv.org/pdf/0909.1899},
         title = {{Time in quantum physics: From an external parameter to an intrinsic observable}},
         url = {http://arxiv.org/abs/0909.1899},
         v1descr = {Thu, 10 Sep 2009 09:46:39 GMT (10kb)},
         year = {2009}
 }
 
 @book{Folland:1989,
         author = {G.B. Folland},
         localfile = {http://space.djvu},
         publisher = {Princeton University Press},
         series = {{Annals of Mathematics Studies}},
         title = {{Harmonic Analysis in Phase Space}},
         year = {1989}
 }
 
 @misc{DabrowskiPiacitelli:2009,
         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.},
         author = {L. Dabrowski and G. Piacitelli},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2009 - Dabrowski, Piacitelli - The k-Minkowski Spacetime: Trace, Classical Limit and uncertainty Relations.pdf},
         month = sep,
         pdf = {http://arxiv.org/pdf/0909.3215},
         title = {{The k-Minkowski Spacetime: Trace, Classical Limit and uncertainty Relations}},
         url = {http://arxiv.org/abs/0909.3215},
         v1descr = {Thu, 17 Sep 2009 14:24:52 GMT (9kb)},
         year = {2009}
 }
 
 @article{FredenhagenRehrenSeiler:2007,
         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.},
         archiveprefix = {arXiv},
         author = {K. Fredenhagen and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren and E. Seiler},
         doi = {10.1007/978-3-540-71117-9_4},
         eprint = {hep-th/0603155},
         journal = {Lect. Notes Phys.},
         localfile = {2006 - Fredenhagen, Rehren, Seiler - Quantum Field Theory: Where We Are.pdf},
         pages = {61--87},
         pdf = {http://arxiv.org/pdf/hep-th/0603155},
         slaccitation = {\%\%CITATION = HEP-TH/0603155\\;\%\%},
         title = {{Quantum Field Theory: Where We Are}},
         url = {http://arxiv.org/abs/hep-th/0603155},
         volume = {721},
         year = {2007}
 }
 
 @book{ConnesCuntzGuentnerHigsonKaminkerRoberts:2000,
         author = {A. Connes and J. Cuntz and E. Guentner and N. Higson and J. Kaminker and J. E. Roberts},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Connes A., Cuntz J., et al., Noncommutative geometry, CIME lectures, 2000, LNM1831, Springer, 2004, 359s.pdf},
         publisher = {Springer},
         series = {{Lecture Notes in Mathematics}},
         title = {{Noncommutative Geometry}},
         year = {2000}
 }
 
 @article{Mueger:1998,
         author = {M. M{\"{u}}ger},
         journal = {Communications in Mathematical Physics},
         localfile = {1998 - M\"{u}ger - Quantum Double Actions on Operator Algebras and Orbifold Quantum Field Theories.pdf},
         number = {1},
         pages = {137--181},
         publisher = {Springer},
         title = {{Quantum double actions on operator algebras and orbifold quantum field theories}},
         volume = {191},
         year = {1998}
 }
 
 @article{AlbeverioMotovilov:2005,
         author = {S. Albeverio and A.K. Motovilov},
         journal = {Preprint},
         localfile = {2005 - Albeverio, Motovilov - Operator integrals with respect to a spectral measure and solutions to some operator equations.pdf},
         title = {{Operator integrals with respect to a spectral measure and solutions to some operator equations}},
         year = {2005}
 }
 
 @book{Pedersen:1979,
         author = {G.K. Pedersen},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Pedersen G.K. C-algebras and their authomorphism groups (AP, 1979)(600dpi)(T)(ISBN 0125494505)(426s).djvu},
         publisher = {Academic Press},
         title = {{C*-Algebras and their Automorphism Groups}},
         year = {1979}
 }
 
 @article{Moschella:2005,
         author = {U. Moschella},
         journal = {Seminaire Poincare},
         localfile = {2005 - Moschella - The de Sitter and anti-de Sitter sightseeing tour.pdf},
         number = {1},
         pages = {1--12},
         title = {{The de Sitter and anti-de Sitter Sightseeing Tour}},
         year = {2005}
 }
 
 @article{BuchholzLechnerSummers:2010,
         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.},
         author = {D. Buchholz and G. Lechner and S. J. Summers},
         doi = {10.1007/s00220-010-1137-1},
         journal = {Commun. Math. Phys.},
         keywords = {kw:NC-Wick; kw:warping; Mathematical Physics (math-ph); Operator Algebras (math.OA); Quantum Physics (quant-ph)},
         localfile = {2010 - Buchholz, Lechner, Summers - Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories.pdf},
         pages = {95--123},
         pdf = {http://arxiv.org/pdf/1005.2656},
         title = {{Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories}},
         url = {http://arxiv.org/abs/1005.2656},
         v1descr = {Sat, 15 May 2010 08:35:06 GMT (33kb)},
         volume = {304},
         x-color = {#199bff},
         year = {2011}
 }
 
 @article{DappiaggiLechnerMorfaMorales:2010,
         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.},
         author = {C. Dappiaggi and G. Lechner and E. Morfa-Morales},
         doi = {10.1007/s00220-011-1210-4},
         journal = {Commun. Math. Phys.},
         keywords = {kw:warping},
         localfile = {2010 - Dappiaggi, Lechner, Morfa-Morales - Deformations of quantum field theories on spacetimes with Killing fields.pdf},
         number = {1},
         pages = {99--130},
         title = {{Deformations of quantum field theories on spacetimes with Killing fields}},
         url = {http://arxiv.org/abs/1006.3548},
         volume = {305},
         x-color = {#199bff},
         year = {2011}
 }
 
 @article{Lechner:2009-1,
         author = {G. Lechner},
         journal = {Proceedings of the ICMP 2009, Prague},
         localfile = {2009 - Lechner - Deformations of Operator Algebras and the Construction of Quantum Field Theories.pdf},
         title = {{Deformations of Operator Algebras and the Construction of Quantum Field Theories}},
         x-color = {#199bff},
         year = {2009}
 }
 
 @article{Doplicher:2009,
         author = {S. Doplicher},
         journal = {Prerint},
         localfile = {2009 - Doplicher - The Principle of Locality. Effectiveness, fate and challenges.pdf},
         title = {{The Principle of Locality. Effectiveness, fate and challenges}},
         url = {http://arxiv.org/abs/0911.5136},
         year = {2009}
 }
 
 @book{Waldmann:2007,
         author = {S. Waldmann},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Waldmann - Poisson-Geometrie und Deformationsquantisierung.pdf},
         publisher = {Springer},
         title = {{Poisson-Geometrie und Deformationsquantisierung}},
         year = {2007}
 }
 
 @article{DappiaggiMorettiPinamonti:2009,
         author = {C. Dappiaggi and V. Moretti and N. Pinamonti},
         journal = {Commun. Math. Phys.},
         localfile = {2007 - Dappiaggi, Moretti, Pinamonti - Cosmological horizons and reconstruction of quantum field theories.pdf},
         pages = {1129},
         title = {{Cosmological horizons the reconstruciton of quantum field theories}},
         url = {http://arxiv.org/abs/0712.1770},
         volume = {285},
         year = {2009}
 }
 
 @article{DappiaggiMorettiPinamonti:2009-1,
         author = {C. Dappiaggi and V. Moretti and N. Pinamonti},
         journal = {J. Math. Phys.},
         localfile = {2008 - Dappiaggi, Moretti, Pinamonti - Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property.pdf},
         pages = {062304},
         title = {{Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property}},
         volume = {50},
         year = {2009}
 }
 
 @article{Manchak:2009,
         author = {J.B. Manchak},
         journal = {Gen. Relativ. Gravit.},
         localfile = {2009 - Manchak - Is spacetime hole free.pdf},
         number = {7},
         pages = {1639--1643},
         publisher = {Springer},
         title = {{Is spacetime hole-free?}},
         volume = {41},
         year = {2009}
 }
 
 @article{Kuckert:2000,
         author = {B. Kuckert},
         journal = {Commun. Math. Phys.},
         localfile = {2000 - Kuckert - Localization Regions of Local Observables.pdf},
         number = {1},
         pages = {197--216},
         publisher = {Springer},
         title = {{Localization regions of local observables}},
         volume = {215},
         year = {2000}
 }
 
 @article{Masiello:1994,
         author = {A. Masiello},
         localfile = {1994 - Masiello - Convex regions of Lorentzian manifolds.pdf},
         title = {{Convex regions of Lorentzian manifolds}},
         year = {1994}
 }
 
 @article{CagnacheDAndreaMartinettiWallet:2009,
         author = {E. Cagnache and F. D'Andrea and P. Martinetti and {{{{{{{{{{{{{{{{{{{{{{{{{J.-C.}}}}}}}}}}}}}}}}}}}}}}}}} Wallet},
         journal = {Preprint},
         localfile = {2009 - Cagnache, D'Andrea, Martinetti, Wallet - The spectral distance on the Moyal plane.pdf},
         title = {{The spectral distance on the Moyal plane}},
         url = {http://arxiv.org/abs/0912.0906},
         year = {2009}
 }
 
 @article{LongoMartinettiRehren:2009,
         author = {R. Longo and P. Martinetti and {{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         journal = {Preprint},
         keywords = {CGMA},
         localfile = {2009 - Longo, Martinetti, Rehren - Geometric modular action for disjoint intervals and boundary conformal field theory.pdf},
         title = {{Geometric modular action for disjoint intervals and boundary conformal field theory}},
         url = {http://arxiv.org/abs/0912.1106},
         year = {2009}
 }
 
 @article{SahlmannVerch:2000,
         author = {H. Sahlmann and R. Verch},
         journal = {Commun. Math. Phys.},
         localfile = {2000 - Sahlmann, Verch - Passivity and microlocal spectrum condition.pdf},
         number = {3},
         pages = {705--731},
         publisher = {Springer},
         title = {{Passivity and microlocal spectrum condition}},
         url = {http://arxiv.org/abs/math-ph/0002021},
         volume = {214},
         year = {2000}
 }
 
 @article{BorchersBuchholz:1999,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers and D. Buchholz},
         journal = {Annales Poincare Phys. Theor.},
         localfile = {1999 - Borchers, Buchholz - Global properties of vacuum states in de Sitter space.pdf},
         pages = {23--40},
         title = {{Global properties of vacuum states in de Sitter space}},
         url = {http://arxiv.org/abs/gr-qc/9803036},
         volume = {A70},
         year = {1999}
 }
 
 @book{Wald:1984,
         author = {R. M. Wald},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Wald R.M. General relativity (1984)(T)(ISBN 0226870332)(494s).djvu},
         publisher = {University of Chicago Press},
         title = {{General Relativity}},
         year = {1984}
 }
 
 @article{Borchers:2009,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         journal = {Preprint},
         localfile = {2009 - Borchers - On the Net of von Neumann algebras associated with a Wedge and Wedge-causal Manifolds.pdf},
         title = {{On the Net of von Neumann algebras associated with a Wedge and Wedge-causal Manifolds}},
         url = {http://www.lqp.uni-goe.de/papers/09/12/09120802.html},
         year = {2009}
 }
 
 @phdthesis{Claessens:2007,
         author = {L. Claessens},
         localfile = {2009 - Claessens - Locally anti de Sitter spaces and deformation quantization.pdf},
         school = {Louvain},
         title = {{Locally anti de Sitter spaces and deformation quantization}},
         year = {2007}
 }
 
 @article{OhlSchenkel:2009,
         author = {T. Ohl and A. Schenkel},
         journal = {Preprint},
         localfile = {2009 - Ohl, Schenkel - Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes.pdf},
         title = {{Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes}},
         url = {http://arxiv.org/abs/0912.2252},
         year = {2009}
 }
 
 @book{SachsWu:1977,
         author = {R.K. Sachs and H. Wu},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Sachs R.K., Wu H. General relativity for mathematicians (Springer, 1977)(T)(ISBN 038790218X)(301s).djvu},
         publisher = {Springer},
         title = {{General relativity for mathematicians}},
         year = {1977}
 }
 
 @misc{Streater:2010,
         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.},
         author = {R. F. Streater},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2010 - Streater - A Scattering Theory based on Free Fields.pdf},
         month = jan,
         pdf = {http://arxiv.org/pdf/1001.1882},
         title = {{A Scattering Theory Based on Free Fields}},
         url = {http://arxiv.org/abs/1001.1882},
         v1descr = {Tue, 12 Jan 2010 13:41:20 GMT (10kb)},
         year = {2010}
 }
 
 @book{Sakai:1971,
         author = {S. Sakai},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Sakai S. C-star-algebras and W-star-algebras (Springer, 1971)(600dpi)(T)(270s).djvu},
         publisher = {Springer},
         title = {{C*-Algebras and W*-Algebras}},
         year = {1971}
 }
 
 @book{Arveson:1976,
         author = {W. Arveson},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Arveson W. An invitation to C-algebras (Springer, 1976)(600dpi)(T)(116s).djvu},
         publisher = {Springer},
         title = {{An Invitation to C*-Algebras}},
         year = {1976}
 }
 
 @article{ArakiWoods:1966,
         author = {H. Araki and J. Woods},
         journal = {Publ. RIMS, Kyoto University},
         localfile = {1966 - Araki, Woods - Complete Boolean algebras of type I factors.pdf},
         pages = {157--242},
         title = {{Complete Boolean algebras of type I factors}},
         volume = {A2},
         year = {1966}
 }
 
 @book{Guichardet:1972,
         author = {A. Guichardet},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Guichardet. Symmetric Hilbert Spaces and Related Topics (LNM0261, Springer, 1972)(ISBN 3540058036)(T)(202s).djvu},
         publisher = {Springer},
         title = {{Symmetric Hilbert Spaces and Related Topics}},
         year = {1972}
 }
 
 @misc{LangvikZahabi:2010,
         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.},
         author = {M. L{\aa}ngvik and A. Zahabi},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2010 - L{\aa}ngvik, Zahabi - On Finite Noncommutativity in Quantum Field Theory.pdf},
         month = feb,
         pdf = {http://arxiv.org/pdf/1002.0956},
         title = {{On Finite Noncommutativity in Quantum Field Theory}},
         url = {http://arxiv.org/abs/1002.0956},
         v1descr = {Thu, 4 Feb 2010 12:44:06 GMT (15kb)},
         year = {2010}
 }
 
 @phdthesis{Porrmann:2000,
         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.},
         author = {M. Porrmann},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2000 - Porrmann - The Concept of Particle Weights in Local Quantum Field Theory - PhD-Thesis.pdf},
         month = may,
         pdf = {http://arxiv.org/pdf/hep-th/0005057},
         title = {{The Concept of Particle Weights in Local Quantum Field Theory}},
         url = {http://arxiv.org/abs/hep-th/0005057},
         v1descr = {Sat, 6 May 2000 13:30:57 GMT (123kb)},
         year = {2000}
 }
 
 @phdthesis{Sanders:2008,
         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.},
         author = {K. Sanders},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {2008 - Sanders - Aspects of locally covariant quantum field theory - PhD-Thesis.pdf},
         month = sep,
         pdf = {http://arxiv.org/pdf/0809.4828},
         school = {University of York},
         title = {{Aspects of locally covariant quantum field theory}},
         url = {http://arxiv.org/abs/0809.4828},
         v1descr = {Sun, 28 Sep 2008 08:45:31 GMT (117kb,D)},
         year = {2008}
 }
 
 @misc{Sanders:2009,
         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.},
         author = {K. Sanders},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {2009 - Sanders - Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime.pdf},
         month = mar,
         pdf = {http://arxiv.org/pdf/0903.1021},
         title = {{Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime}},
         url = {http://arxiv.org/abs/0903.1021},
         v1descr = {Thu, 5 Mar 2009 15:33:03 GMT (19kb)},
         year = {2009}
 }
 
 @article{Sanders:2009-1,
         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.},
         author = {K. Sanders},
         journal = {Commun. Math. Phys.},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {2008 - Sanders - On the Reeh-Schlieder Property in Curved Spacetime.pdf},
         pages = {271--285},
         pdf = {http://arxiv.org/pdf/0801.4676},
         title = {{On the Reeh-Schlieder Property in Curved Spacetime}},
         url = {http://arxiv.org/abs/0801.4676},
         v1descr = {Wed, 30 Jan 2008 14:01:50 GMT (18kb)},
         volume = {288},
         year = {2009}
 }
 
 @techreport{DappiaggiPinamontiPorrmann:2010,
         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'.},
         author = {C. Dappiaggi and N. Pinamonti and M. Porrmann},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2010 - Dappiaggi, Pinamonti, Porrmann - Local causal structures, Hadamard states and the principle of local covariance in quantum field theory.pdf},
         month = jan,
         number = {Desy 10-001, ESI 2203, ZMP-HH/09-33},
         pdf = {http://arxiv.org/pdf/1001.0858},
         title = {{Local causal structures, Hadamard states and the principle of local covariance in quantum field theory}},
         url = {http://arxiv.org/abs/1001.0858},
         v1descr = {Wed, 6 Jan 2010 11:07:03 GMT (45kb)},
         year = {2010}
 }
 
 @article{Pinamonti:2009,
         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.},
         author = {N. Pinamonti},
         doi = {10.1007/s00220-009-0780-x},
         journal = {Commun. Math. Phys.},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2008 - Pinamonti - Conformal generally covariant quantum field theory: The scalar field and its Wick products.pdf},
         pages = {1117--1135},
         pdf = {http://arxiv.org/pdf/0806.0803},
         title = {{Conformal generally covariant quantum field theory: The scalar field and its Wick products}},
         url = {http://arxiv.org/abs/0806.0803},
         v1descr = {Wed, 4 Jun 2008 15:24:27 GMT (19kb)},
         v1url = {http://www.arxiv.org/abs/0806.0803v1},
         v2descr = {Tue, 3 Feb 2009 09:34:30 GMT (22kb)},
         volume = {288},
         year = {2009}
 }
 
 @lecturenotes{Waldmann:2009,
         author = {S. Waldmann},
         localfile = {2009 - Waldmann - Geometric Wave Equations.pdf},
         title = {{Geometric Wave Equations}},
         year = {2009}
 }
 
 @phdthesis{LauridsenRibeiro:2007,
         author = {P. Lauridsen-Ribeiro},
         localfile = {2007 - Lauridsen-Ribeiro - Structural and Dynamical Aspects of the AdS-CFT Correspondence - a Rigorous Approach - PhD-Thesis.pdf},
         school = {Sao Paulo},
         title = {{Structural and Dynamical Aspects of the AdS/CFT Correspondence: a Rigorous Approach}},
         url = {http://arxiv.org/abs/0712.0401},
         year = {2007}
 }
 
 @book{Jaenich:1993,
         author = {K. J{\"{a}}nich},
         edition = {2},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Jaenich K. Vektoranalysis (2ed., Springer, 1993)(de)(L)(T)(ISBN 3540571426)(143s).djvu},
         publisher = {Springer},
         title = {{Vektoranalysis}},
         year = {1993}
 }
 
 @book{Isham:2001,
         author = {C. J. Isham},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Isham C.J. Modern Differential Geometry for Physicists (WS, 2001)(T)(306s).djvu},
         publisher = {World Scientific},
         title = {{Modern Differential Geometry for Physicists}},
         year = {2001}
 }
 
 @book{Janich:1999,
         author = {K. J{\"{a}}nich},
         edition = {6},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/J\"{a}nich - Topologie.djvu},
         publisher = {Springer},
         title = {{Topologie}},
         year = {1999}
 }
 
 @book{Rudin:1991,
         author = {W. Rudin},
         edition = {2},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Rudin - Functional Analysis.djvu},
         publisher = {McGraw-Hill},
         title = {{Functional Analysis}},
         year = {1991}
 }
 
 @misc{Longo:2000,
         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.},
         author = {R. Longo},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2000 - Longo - The Bisognano-Wichmann Theorem for Charged States and the Conformal Boundary of a Black Hole.pdf},
         month = jan,
         pdf = {http://arxiv.org/pdf/math-ph/0001034},
         title = {{The Bisognano-Wichmann Theorem for Charged States and the Conformal Boundary of a Black Hole}},
         url = {http://arxiv.org/abs/math-ph/0001034},
         v1descr = {Fri, 21 Jan 2000 19:40:21 GMT (8kb)},
         year = {2000}
 }
 
 @book{GalindoPascual:1990,
         author = {A. Galindo and P. Pascual},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Galindo A., Pascual P. Quantum mechanics I (Springer, 1990)(ISBN 0387514066)(T) (431s).djvu},
         publisher = {Springer},
         title = {{Quantum Mechanics I}},
         year = {1990}
 }
 
 @book{GalindoPascual:1991,
         author = {A. Galindo and P. Pascual},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Galindo A., Pascual P. Quantum mechanics II (Springer, 1991)(ISBN 038752309X)(T)(388s).djvu},
         publisher = {Springer},
         title = {{Quantum Mechanics II}},
         year = {1991}
 }
 
 @book{O'Neill:1983,
         author = {B. O'Neill},
         localfile = {http://geometry.djvu},
         publisher = {Academic Press},
         title = {{Semi-Riemannian Geometry}},
         year = {1983}
 }
 
 @book{Jost:2005,
         author = {J. Jost},
         localfile = {http://analysis.djvu},
         publisher = {Springer},
         title = {{Postmodern Analysis}},
         year = {2005}
 }
 
 @book{AbdallaAbdallaRothe:1991,
         author = {E. Abdalla and C. Abdalla and K.D. Rothe},
         localfile = {http://qft.djvu},
         publisher = {World Scientific},
         title = {{Non-perturbative methods in 2-dimensional quantum field theory}},
         year = {1991}
 }
 
 @article{BernalSanchez:2005,
         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 $M$.},
         author = {A. N. Bernal and M. S{\'{a}}nchez},
         doi = {10.1007/s00220-005-1346-1},
         journal = {Commun. Math. Phys.},
         keywords = {Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc)},
         localfile = {2005 - Bernal, Sanchez - Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes.pdf},
         pages = {43--50},
         pdf = {http://arxiv.org/pdf/gr-qc/0401112},
         title = {{Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes}},
         url = {http://arxiv.org/abs/gr-qc/0401112},
         v1descr = {Wed, 28 Jan 2004 16:38:07 GMT (9kb)},
         v1url = {http://www.arxiv.org/abs/gr-qc/0401112v1},
         v2descr = {Thu, 4 Nov 2004 11:20:09 GMT (9kb)},
         v2url = {http://www.arxiv.org/abs/gr-qc/0401112v2},
         v3descr = {Tue, 15 Feb 2005 18:45:19 GMT (10kb)},
         volume = {257},
         year = {2005}
 }
 
 @article{BernalSanchez:2006,
         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).},
         author = {A. N. Bernal and M. S{\'{a}}nchez},
         doi = {10.1007/s11005-006-0091-5},
         journal = {Lett.Math.Phys.},
         keywords = {Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc)},
         localfile = {2006 - Bernal, Sanchez - Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions.pdf},
         pages = {183--197},
         pdf = {http://arxiv.org/pdf/gr-qc/0512095},
         title = {{Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions}},
         url = {http://arxiv.org/abs/gr-qc/0512095},
         v1descr = {Thu, 15 Dec 2005 18:57:39 GMT (180kb)},
         volume = {77},
         year = {2006}
 }
 
 @book{SeifertThrelfall:1980,
         author = {H. Seifert and W. Threlfall},
         localfile = {http://topology.djvu},
         publisher = {Academic Press},
         title = {{A Textbook of Topology}},
         year = {1980}
 }
 
 @book{Chandrasekhar:1983,
         author = {S. Chandrasekhar},
         localfile = {http://holes.djvu},
         publisher = {Oxford University Press},
         title = {{The mathematical theory of black holes}},
         year = {1983}
 }
 
 @article{ChandrasekharFerrari:1984,
         author = {S. Chandrasekhar and V. Ferrari},
         journal = {Proc. Roy. Soc. Lond.},
         pages = {55},
         slaccitation = {\%\%CITATION = PRSLA,A396,55\\;\%\%},
         title = {{On the Nutku-Halil solution for colliding impulsive gravitational waves}},
         volume = {A396},
         year = {1984}
 }
 
 @article{Ellis:2006,
         author = {G. F. R. Ellis},
         doi = {10.1007/s10714-006-0283-4},
         journal = {Gen. Rel. Grav.},
         localfile = {2006 - Ellis - The Bianchi Models - Then and Now.pdf},
         pages = {1003--1015},
         slaccitation = {\%\%CITATION = GRGVA,38,1003\\;\%\%},
         title = {{The Bianchi models: Then and now}},
         volume = {38},
         year = {2006}
 }
 
 @article{FullingParkerHu:1974,
         author = {S. A. Fulling and L. Parker and B. L. Hu},
         doi = {10.1103/PhysRevD.10.3905},
         journal = {Phys. Rev.},
         pages = {3905--3924},
         slaccitation = {\%\%CITATION = PHRVA,D10,3905\\;\%\%},
         title = {{Conformal energy-momentum tensor in curved spacetime: Adiabatic regularization and renormalization}},
         volume = {D10},
         year = {1974}
 }
 
 @book{BarGinouxPfaffle:2007,
         author = {C. B{\"{a}}r and N. Ginoux and F. Pf{\"{a}}ffle},
         publisher = {European Mathematical Society},
         title = {{Wave Equations on Lorentzian Manifolds and Quantization}},
         year = {2007}
 }
 
 @book{Wald:1994,
         author = {R. M. Wald},
         localfile = {http://thermodynamics.djvu},
         publisher = {Chicago University Press},
         title = {{Quantum field theory in curved space-time and black hole thermodynamics}},
         year = {1994}
 }
 
 @article{Radzikowski:1996,
         author = {M. J. Radzikowski},
         doi = {10.1007/BF02101180},
         journal = {Commun. Math. Phys.},
         pages = {1--22},
         slaccitation = {\%\%CITATION = CMPHA,180,1\\;\%\%},
         title = {{A Local to global singularity theorem for quantum field theory on curved space-time}},
         volume = {180},
         year = {1996}
 }
 
 @article{Radzikowski:1996-1,
         author = {M. J. Radzikowski},
         doi = {10.1007/BF02100096},
         journal = {Commun. Math. Phys.},
         pages = {529--553},
         slaccitation = {\%\%CITATION = CMPHA,179,529\\;\%\%},
         title = {{Micro-local approach to the Hadamard condition in quantum field theory on curved space-time}},
         volume = {179},
         year = {1996}
 }
 
 @article{AllenFolacci:1987,
         author = {B. Allen and A. Folacci},
         doi = {10.1103/PhysRevD.35.3771},
         journal = {Phys. Rev.},
         pages = {3771},
         slaccitation = {\%\%CITATION = PHRVA,D35,3771\\;\%\%},
         title = {{The massless minimally coupled scalar field in de Sitter space}},
         volume = {D35},
         year = {1987}
 }
 
 @article{Geroch:1968,
         author = {R. P. Geroch},
         doi = {10.1063/1.1664507},
         journal = {J. Math. Phys.},
         pages = {1739--1744},
         slaccitation = {\%\%CITATION = JMAPA,9,1739\\;\%\%},
         title = {{Spinor structure of space-times in general relativity. I}},
         volume = {9},
         year = {1968}
 }
 
 @article{Geroch:1970,
         author = {R. P. Geroch},
         doi = {10.1063/1.1665067},
         journal = {J. Math. Phys.},
         pages = {343--348},
         slaccitation = {\%\%CITATION = JMAPA,11,343\\;\%\%},
         title = {{Spinor structure of space-times in general relativity. II}},
         volume = {11},
         year = {1970}
 }
 
 @book{HawkingEllis:1973,
         author = {S. Hawking and G. F. R. Ellis},
         localfile = {http://spacetime.djvu},
         publisher = {Cambridge University Press},
         title = {{The large scale structure of space-time}},
         year = {1973}
 }
 
 @book{Higham:,
         author = {N. J. Higham},
         localfile = {http://sciences.djvu},
         publisher = {SIAM},
         title = {{Handbook of Writing for the Mathematical Sciences}},
         year = {1998}
 }
 
 @article{Rehren:2000,
         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.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{K.-H.}}}}}}}}}}}}}}}}}}}}}}}}} Rehren},
         journal = {Annales Henri Poincare},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
         localfile = {1999 - Rehren - Algebraic Holography.pdf},
         pages = {607--623},
         pdf = {http://arxiv.org/pdf/hep-th/9905179},
         title = {{Algebraic Holography}},
         url = {http://arxiv.org/abs/hep-th/9905179},
         v1descr = {Tue, 25 May 1999 13:32:37 GMT (21kb)},
         v1url = {http://www.arxiv.org/abs/hep-th/9905179v1},
         v2descr = {Tue, 1 Jun 1999 09:10:35 GMT (22kb)},
         v2url = {http://www.arxiv.org/abs/hep-th/9905179v2},
         v3descr = {Tue, 10 Aug 1999 12:11:45 GMT (25kb)},
         v3url = {http://www.arxiv.org/abs/hep-th/9905179v3},
         v4descr = {Thu, 7 Oct 1999 12:18:56 GMT (26kb)},
         volume = {1},
         year = {2000}
 }
 
 @article{Keyl:1996,
         author = {M. Keyl},
         doi = {10.1142/S0129055X96000093},
         journal = {Rev. Math. Phys.},
         pages = {229--270},
         slaccitation = {\%\%CITATION = RMPHE,8,229\\;\%\%},
         title = {{Causal spaces, causal complements and their relations to quantum field theory}},
         volume = {8},
         year = {1996}
 }
 
 @article{Buchholz:2000,
         archiveprefix = {arXiv},
         author = {D. Buchholz},
         eprint = {math-ph/0011044},
         journal = {Preprint},
         localfile = {2000 - Buchholz - Algebraic quantum field theory: A Status report.pdf},
         slaccitation = {\%\%CITATION = MATH-PH/0011044\\;\%\%},
         title = {{Algebraic quantum field theory: A status report}},
         year = {2000}
 }
 
 @article{Kay:1985,
         author = {B. S. Kay},
         doi = {10.1007/BF01212687},
         journal = {Commun. Math. Phys.},
         localfile = {1985 - Kay - The double-wedge algebra for quantum fields on Schwarzschild and Minkowski spacetimes.pdf},
         pages = {57},
         slaccitation = {\%\%CITATION = CMPHA,100,57\\;\%\%},
         title = {{The double-wedge algebra for quantum fields on Schwarzschild and Minkowski space-times}},
         url = {http://projecteuclid.org/euclid.cmp/1103943337},
         volume = {100},
         year = {1985}
 }
 
 @article{Bieliavsky:2007,
         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.},
         author = {P. Bieliavsky},
         journal = {Preprint},
         keywords = {Operator Algebras (math.OA); Quantum Algebra (math.QA); kw:UDF},
         localfile = {2007 - Bieliavsky - Deformation quantization for actions of the affine group.pdf},
         month = sep,
         pdf = {http://arxiv.org/pdf/0709.1110},
         title = {{Deformation quantization for actions of the affine group }},
         url = {http://arxiv.org/abs/0709.1110},
         v1descr = {Fri, 7 Sep 2007 16:27:31 GMT (19kb)},
         year = {2007}
 }
 
 @article{BieliavskyDetournayRoomanSpindel:2004,
         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.$AdS$},
         author = {P. Bieliavsky and S. Detournay and M. Rooman and P. Spindel},
         journal = {JHEP},
         keywords = {High Energy Physics - Theory (hep-th); kw:UDF},
         localfile = {2004 - Bieliavsky, Detournay, Rooman, Spindel - Star products on extended massive non-rotating BTZ black holes.pdf},
         pages = {031},
         pdf = {http://arxiv.org/pdf/hep-th/0403257},
         title = {{Star products on extended massive non-rotating BTZ black holes}},
         url = {http://arxiv.org/abs/hep-th/0403257},
         v1descr = {Thu, 25 Mar 2004 18:06:41 GMT (289kb)},
         volume = {0406},
         year = {2004}
 }
 
 @misc{BieliavskyMassar:2001,
         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.},
         author = {P. Bieliavsky and M. Massar},
         keywords = {Differential Geometry (math.DG); kw:UDF; Mathematical Physics (math-ph); Quantum Algebra (math.QA); Symplectic Geometry (math.SG)},
         localfile = {2001 - Bieliavsky, Massar - Strict Deformation Quantization for Actions of a Class of Symplectic Lie Groups.pdf},
         month = jan,
         pdf = {http://arxiv.org/pdf/math/0011144},
         title = {{Strict Deformation Quantization for Actions of a Class of Symplectic Lie Groups}},
         url = {http://arxiv.org/abs/math/0011144},
         v1descr = {Mon, 20 Nov 2000 20:36:43 GMT (17kb)},
         v1url = {http://www.arxiv.org/abs/math/0011144v1},
         v2descr = {Thu, 23 Nov 2000 20:23:42 GMT (17kb)},
         v2url = {http://www.arxiv.org/abs/math/0011144v2},
         v3descr = {Mon, 15 Jan 2001 19:11:46 GMT (17kb)},
         year = {2001}
 }
 
 @book{Nachbin:1964,
         author = {L. Nachbin},
         localfile = {http://integral.djvu},
         title = {{The Haar Integral}},
         year = {1964}
 }
 
 @article{LongoWitten:2010,
         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.},
         author = {R. Longo and E. Witten},
         journal = {Preprint},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Operator Algebras (math.OA)},
         localfile = {2010 - Longo, Witten - An Algebraic Construction of Boundary Quantum Field Theory.pdf},
         month = apr,
         pdf = {http://arxiv.org/pdf/1004.0616},
         title = {{An Algebraic Construction of Boundary Quantum Field Theory }},
         url = {http://arxiv.org/abs/1004.0616},
         v1descr = {Mon, 5 Apr 2010 11:49:22 GMT (21kb)},
         year = {2010}
 }
 
 @article{Araki:1971,
         author = {H. Araki},
         doi = {10.2977/prims},
         eprint = {projecteuclid},
         journal = {Publ. Res. Inst. Math. Sci. Kyoto},
         localfile = {1970 - Araki - On Quasifree States of CAR and Bogoliubov Automorphisms.pdf},
         pages = {385--442},
         slaccitation = {\%\%CITATION = PBMAA,6,385\\;\%\%},
         title = {{On quasifree states of CAR and Bogoliubov automorphisms}},
         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},
         volume = {6},
         year = {1971}
 }
 
 @article{Araki:1968,
         author = {H. Araki},
         journal = {Publ. Res. Inst. Math. Sci. Kyoto University, Ser. A},
         localfile = {1968 - Araki - On the Diagonalization of a Bilinear Hamiltonian by a Bogoliubov Transformation.pdf},
         pages = {387--412},
         title = {{On the diagonalization of a bilinear Hamiltonian by a Bogoliubov transformation}},
         volume = {4},
         year = {1968}
 }
 
 @article{DappiaggiHackPinamonti:2009,
         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.},
         author = {C. Dappiaggi and {{{{{{{{{{{{{{{{{{{{{{{{{T.-P.}}}}}}}}}}}}}}}}}}}}}}}}} Hack and N. Pinamonti},
         doi = {10.1142/S0129055X09003864},
         journal = {Rev. Math. Phys.},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2009 - Dappiaggi, Hack, Pinamonti - The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor.pdf},
         pages = {1241--1312},
         pdf = {http://arxiv.org/pdf/0904.0612},
         title = {{The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor}},
         url = {http://arxiv.org/abs/0904.0612},
         v1descr = {Fri, 3 Apr 2009 16:08:54 GMT (64kb)},
         volume = {21},
         year = {2009}
 }
 
 @article{Dimock:1982,
         author = {J. Dimock},
         coden = {TAMTAM},
         doi = {10.2307/1998597},
         fjournal = {Transactions of the American Mathematical Society},
         issn = {0002-9947},
         journal = {Trans. Amer. Math. Soc.},
         localfile = {1982 - Dimock - Dirac Quantum Fields on a Manifold.pdf},
         mrclass = {81E20 (46L60 81E05)},
         mrnumber = {MR637032 (83b:81109)},
         mrreviewer = {Ivan F. Wilde},
         number = {1},
         pages = {133--147},
         title = {{Dirac quantum fields on a manifold}},
         volume = {269},
         year = {1982}
 }
 
 @article{Strohmaier:2000-1,
         archiveprefix = {arXiv},
         author = {A. Strohmaier},
         doi = {10.1007/s002200000299},
         eprint = {math-ph/0002054},
         journal = {Commun. Math. Phys.},
         localfile = {2000 - Strohmaier - The Reeh--Schlieder Property for Quantum Fields on Stationary Spacetimes.pdf},
         pages = {105--118},
         slaccitation = {\%\%CITATION = MATH-PH/0002054\\;\%\%},
         title = {{The Reeh-Schlieder property for quantum fields on stationary spacetimes}},
         volume = {215},
         year = {2000}
 }
 
 @article{ArakiWyss:1964,
         author = {H. Araki and W. Wyss},
         journal = {Helv. Phys. Acta},
         pages = {136},
         title = {{Representations of canonical anticommutation relations}},
         volume = {37},
         year = {1964}
 }
 
 @article{DoplicherHaagRoberts:1969,
         author = {S. Doplicher and R. Haag and J. E. Roberts},
         journal = {Commun. Math. Phys.},
         localfile = {1969 - Doplicher, Haag, Roberts - Fields, observables and gauge transformations I.pdf},
         pages = {1--23},
         slaccitation = {\%\%CITATION = CMPHA,13,1\\;\%\%},
         title = {{Fields, observables and gauge transformations. I}},
         url = {http://projecteuclid.org/euclid.cmp/1103841481},
         volume = {13},
         year = {1969}
 }
 
 @article{Foit:1983,
         author = {J. J. Foit},
         journal = {Publ. Res. Inst. Math. Sci. Kyoto},
         localfile = {1983 - Foit - Abstract Twisted Duality for Quantum Free Fermi Fields.pdf},
         pages = {729--741},
         slaccitation = {\%\%CITATION = PBMAA,19,729\\;\%\%},
         title = {{Abstract Twisted Duality for Quantum Free Fermi Fields}},
         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},
         volume = {19},
         year = {1983}
 }
 
 @article{Summers:1982,
         author = {S. J. Summers},
         doi = {10.1007/BF01205664},
         journal = {Commun. Math. Phys.},
         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},
         pages = {111--141},
         slaccitation = {\%\%CITATION = CMPHA,86,111\\;\%\%},
         title = {{Normal product states for fermions and twisted duality for CCR- and CAR-type algebras with application to the Yukawa2 quantum field model}},
         volume = {86},
         year = {1982}
 }
 
 @article{Verch:2001,
         archiveprefix = {arXiv},
         author = {R. Verch},
         doi = {10.1007/s002200100526},
         eprint = {math-ph/0102035},
         journal = {Commun. Math. Phys.},
         localfile = {2001 - Verch - A Spin-Statistics Theorem for Quantum Fields on Curved Spacetime Manifolds in a Generally Covariant Framework.pdf},
         pages = {261--288},
         slaccitation = {\%\%CITATION = MATH-PH/0102035\\;\%\%},
         title = {{A spin-statistics theorem for quantum fields on curved spacetime manifolds in a generally covariant framework}},
         volume = {223},
         year = {2001}
 }
 
 @article{Verch:2001-1,
         archiveprefix = {arXiv},
         author = {R. Verch},
         eprint = {math-ph/0011026},
         journal = {Fields Inst. Commun.},
         localfile = {2000 - Verch - On Generalizations of the Spectrum Condition.pdf},
         pages = {409--428},
         slaccitation = {\%\%CITATION = MATH-PH/0011026\\;\%\%},
         title = {{On generalizations of the spectrum condition}},
         volume = {30},
         year = {2001}
 }
 
 @article{Schweitzer:1993,
         author = {L. B. Schweitzer},
         doi = {10.1142/S0129167X93000315},
         fjournal = {International Journal of Mathematics},
         issn = {0129-167X},
         journal = {Internat. J. Math.},
         localfile = {1993 - Schweitzer - Dense m-convex Frechet Subalgebras of Operator Algebra Crossed Products by Lie Groups.pdf},
         mrclass = {46K99 (46A11 46E25 46L05 46L55)},
         mrnumber = {MR1232986 (94g:46058)},
         mrreviewer = {Keith Taylor},
         number = {4},
         pages = {601--673},
         title = {{Dense {$m$}-convex {F}r\'{e}chet subalgebras of operator algebra crossed products by {L}ie groups}},
         url = {http://dx.doi.org/10.1142/S0129167X93000315},
         volume = {4},
         year = {1993}
 }
 
 @book{Taylor:1986,
         author = {M. E. Taylor},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Taylor - Noncommutative Harmonic Analysis.pdf},
         publisher = {American Mathematical Society},
         title = {{Noncommutative Harmonic Analysis}},
         year = {1986}
 }
 
 @misc{Keyl:2002,
         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.},
         author = {M. Keyl},
         keywords = {Quantum Physics (quant-ph)},
         localfile = {2008 - Keyl - Fundamentals of Quantum Information Theory.pdf},
         month = feb,
         pdf = {http://arxiv.org/pdf/quant-ph/0202122},
         title = {{Fundamentals of Quantum Information Theory}},
         url = {http://arxiv.org/abs/quant-ph/0202122},
         v1descr = {Thu, 21 Feb 2002 16:52:04 GMT (154kb)},
         year = {2002}
 }
 
 @article{PaschkeVerch:2004,
         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.},
         author = {M. Paschke and R. Verch},
         journal = {Class.Quant.Grav.},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2004 - Paschke, Verch - Local covariant quantum field theory over spectral geometries.pdf},
         pages = {5299--5316},
         pdf = {http://arxiv.org/pdf/gr-qc/0405057},
         title = {{Local covariant quantum field theory over spectral geometries}},
         url = {http://arxiv.org/abs/gr-qc/0405057},
         v1descr = {Tue, 11 May 2004 17:05:57 GMT (28kb)},
         volume = {21},
         year = {2004}
 }
 
 @article{Zahn:2010,
         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.},
         author = {Jochen Zahn},
         journal = {Annales Henri Poincare},
         keywords = {High Energy Physics - Theory (hep-th); kw:NC-Wick},
         localfile = {2010 - Zahn - Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential.pdf},
         pages = {777--804},
         pdf = {http://arxiv.org/pdf/1005.0541},
         title = {{Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential}},
         url = {http://arxiv.org/abs/1005.0541},
         v1descr = {Tue, 4 May 2010 14:32:11 GMT (25kb)},
         v1url = {http://www.arxiv.org/abs/1005.0541v1},
         v2descr = {Tue, 3 May 2011 13:51:19 GMT (26kb)},
         volume = {12},
         year = {2011}
 }
 
 @misc{AastrupGrimstrupPaschkeNest:2009,
         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.},
         author = {J. Aastrup and J. M. Grimstrup and M. Paschke and R. Nest},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
         localfile = {2009 - Aastrup, Grimstrup, Paschke, Nest - On Semi-Classical States of Quantum Gravity and Noncommutative Geometry.pdf},
         month = jul,
         pdf = {http://arxiv.org/pdf/0907.5510},
         title = {{On Semi-Classical States of Quantum Gravity and Noncommutative Geometry}},
         url = {http://arxiv.org/abs/0907.5510},
         v1descr = {Fri, 31 Jul 2009 11:25:13 GMT (34kb,D)},
         year = {2009}
 }
 
 @article{AastrupGrimstrupNest:2008,
         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.},
         author = {J. Aastrup and J. M. Grimstrup and R. Nest},
         doi = {10.1088/0264-9381},
         journal = {Class. Quant. Grav.},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
         localfile = {2008 - Aastrup, Grimstrup, Nest - On Spectral Triples in Quantum Gravity.pdf},
         month = feb,
         number = {26},
         pages = {065011},
         pdf = {http://arxiv.org/pdf/0802.1783},
         title = {{On Spectral Triples in Quantum Gravity I}},
         url = {http://arxiv.org/abs/0802.1783},
         v1descr = {Wed, 13 Feb 2008 11:12:49 GMT (76kb)},
         year = {2008}
 }
 
 @article{BlaschkeGieresKronbergerSchwedaWohlgenannt:2008,
         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.},
         author = {D. Blaschke and F. Gieres and E. Kronberger and M. Schweda and M. Wohlgenannt},
         doi = {10.1088/1751-8113},
         journal = {J.Phys.A},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2008 - Blaschke, Gieres, Kronberger, Schweda, Wohlgenannt - Translation-invariant models for non-commutative gauge fields.pdf},
         pages = {252002},
         pdf = {http://arxiv.org/pdf/0804.1914},
         title = {{Translation-invariant models for non-commutative gauge fields}},
         url = {http://arxiv.org/abs/0804.1914},
         v1descr = {Fri, 11 Apr 2008 15:25:50 GMT (8kb)},
         volume = {41},
         year = {2008}
 }
 
 @article{AschieriBlohmannDimitrijevicMeyerSchuppWess:2005,
         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.},
         author = {P. Aschieri and C. Blohmann and M. Dimitrijevic and F. Meyer and P. Schupp and J. Wess},
         doi = {10.1088/0264-9381},
         journal = {Class.Quant.Grav.},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2005 - Aschieri, Blohmann, Dimitrijevic, Meyer, Schupp, Wess - A Gravity Theory on Noncommutative Spaces.pdf},
         pages = {3511--3532},
         pdf = {http://arxiv.org/pdf/hep-th/0504183},
         title = {{A Gravity Theory on Noncommutative Spaces}},
         url = {http://arxiv.org/abs/hep-th/0504183},
         v1descr = {Fri, 22 Apr 2005 13:05:16 GMT (38kb)},
         v1url = {http://www.arxiv.org/abs/hep-th/0504183v1},
         v2descr = {Thu, 12 May 2005 17:52:30 GMT (38kb)},
         v2url = {http://www.arxiv.org/abs/hep-th/0504183v2},
         v3descr = {Tue, 16 Aug 2005 14:38:18 GMT (38kb)},
         volume = {22},
         year = {2005}
 }
 
 @article{OsterwalderSchrader:1975,
         author = {K. Osterwalder and R. Schrader},
         doi = {10.1007/BF01608978},
         journal = {Commun. Math. Phys.},
         keywords = {kw:NC-Wick},
         localfile = {1975 - Osterwalder, Schrader - Axioms for Euclidean Green's functions II.pdf},
         pages = {281},
         slaccitation = {\%\%CITATION = CMPHA,42,281\\;\%\%},
         title = {{Axioms for Euclidean Green's Functions. 2}},
         url = {http://projecteuclid.org/euclid.cmp/1103899050},
         volume = {42},
         x-color = {#19ffd1},
         year = {1975}
 }
 
 @article{Zinoviev:1995,
         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.},
         author = {Yu.M. Zinoviev},
         journal = {Commun. Math. Phys.},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {1995 - Zinoviev - Equivalence of Euclidean and Wightman field theories.pdf},
         pages = {1--28},
         pdf = {http://arxiv.org/pdf/hep-th/9408009},
         title = {{Equivalence of the Euclidean and Wightman Field Theories}},
         url = {http://arxiv.org/abs/hep-th/9408009},
         v1descr = {Tue, 2 Aug 1994 11:15:50 GMT (20kb)},
         volume = {174},
         year = {1995}
 }
 
 @article{BahnsDoplicherFredenhagenPiacitelli:2010,
         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.},
         author = {D. Bahns and S. Doplicher and K. Fredenhagen and G. Piacitelli},
         journal = {Preprint},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)},
         localfile = {2010 - Bahns, Doplicher, Fredenhagen, Piacitelli - Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators.pdf},
         month = may,
         pdf = {http://arxiv.org/pdf/1005.2130},
         title = {{Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators }},
         url = {http://arxiv.org/abs/1005.2130},
         v1descr = {Wed, 12 May 2010 15:34:41 GMT (25kb)},
         year = {2010}
 }
 
 @article{SummersWerner:1987,
         author = {S. J. Summers and R. Werner},
         doi = {10.1063/1.527733},
         journal = {J. Math. Phys.},
         localfile = {1987 - Summers, Werner - Bell's Inequalities and quantum field theory I. General setting.pdf},
         pages = {2440--2447},
         slaccitation = {\%\%CITATION = JMAPA,28,2440\\;\%\%},
         title = {{Bells Inequalities and quantum field theory I. General setting}},
         volume = {28},
         x-color = {#ff9bfa},
         year = {1987}
 }
 
 @misc{Rieffel:1997,
         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.},
         author = {M. A. Rieffel},
         keywords = {Functional Analysis (math.FA); Operator Algebras (math.OA)},
         localfile = {1997 - Rieffel - On the operator algebra for the space-time uncertainty relations.pdf},
         month = jan,
         pdf = {http://arxiv.org/pdf/funct-an/9701011},
         title = {{On the operator algebra for the space-time uncertainty relations}},
         url = {http://arxiv.org/abs/funct-an/9701011},
         v1descr = {Wed, 29 Jan 1997 00:24:41 GMT (10kb)},
         year = {1997}
 }
 
 @book{Lang:1975,
         author = {S. Lang},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Lang - SL(2,R).djvu},
         publisher = {Springer},
         title = {{SL\_2(R)}},
         year = {1975}
 }
 
 @article{BuchholzDAntoniLongo:2007,
         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.},
         author = {D. Buchholz and C. D'Antoni and R. Longo},
         journal = {Commun. Math. Phys.},
         keywords = {Mathematical Physics (math-ph); Operator Algebras (math.OA); kw:scaling},
         localfile = {2006 - Buchholz, D'Antoni, Longo - Nuclearity and Thermal States in Conformal Field Theory.pdf},
         pages = {267--293},
         pdf = {http://arxiv.org/pdf/math-ph/0603083},
         title = {{Nuclearity and Thermal States in Conformal Field Theory}},
         url = {http://arxiv.org/abs/math-ph/0603083},
         v1descr = {Thu, 30 Mar 2006 13:30:28 GMT (25kb)},
         v1url = {http://www.arxiv.org/abs/math-ph/0603083v1},
         v2descr = {Thu, 16 Nov 2006 16:33:11 GMT (26kb)},
         volume = {270},
         year = {2007}
 }
 
 @book{Dixmier:1977,
         address = {Amsterdam, New York, Oxford},
         author = {J. Dixmier},
         localfile = {http://c-algebras.djvu},
         publisher = {North-Holland-Publishing Company},
         title = {{C*-Algebras}},
         year = {1977}
 }
 
 @article{Jaekel:2000,
         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.},
         author = {C. D. J{\"{a}}kel},
         journal = {J.Math.Phys.},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {1999 - J\"{a}kel - The Reeh-Schlieder property for thermal field theories.pdf},
         pages = {1745--1754},
         pdf = {http://arxiv.org/pdf/hep-th/9904049},
         title = {{The Reeh-Schlieder property for thermal field theories}},
         url = {http://arxiv.org/abs/hep-th/9904049},
         v1descr = {Wed, 7 Apr 1999 09:47:22 GMT (13kb)},
         v1url = {http://www.arxiv.org/abs/hep-th/9904049v1},
         v2descr = {Wed, 5 May 2004 08:59:15 GMT (13kb)},
         volume = {41},
         year = {2000}
 }
 
 @article{Sanders:2009-2,
         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.},
         author = {K. Sanders},
         doi = {10.1142/S0129055X10003990},
         journal = {Rev. Math. Phys.},
         keywords = {Mathematical Physics (math-ph)},
         localfile = {2010 - Sanders - The locally covariant Dirac field.pdf},
         number = {4},
         pages = {381--430},
         pdf = {http://arxiv.org/pdf/0911.1304},
         title = {{The locally covariant Dirac field}},
         url = {http://arxiv.org/abs/0911.1304},
         v1descr = {Fri, 6 Nov 2009 17:17:11 GMT (48kb)},
         v1url = {http://www.arxiv.org/abs/0911.1304v1},
         v2descr = {Wed, 11 Nov 2009 14:40:24 GMT (48kb)},
         volume = {22},
         year = {2010}
 }
 
 @article{MukhanovFeldmanBrandenberger:1990,
         author = {V. F. Mukhanov and H. A. Feldman and R. H. Brandenberger},
         doi = {10.1016/0370-1573(92)90044-Z},
         journal = {Phys. Rept.},
         pages = {203--333},
         slaccitation = {\%\%CITATION = PRPLC,215,203\\;\%\%},
         title = {{Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions}},
         volume = {215},
         year = {1992}
 }
 
 @article{EstradaGracia-BondiaVarilly:1989,
         author = {R. Estrada and J. M. Gracia-Bondia and J. C. Varilly},
         doi = {10.1063/1.528514},
         journal = {J. Math. Phys.},
         localfile = {1989 - Estrada, Gracia-Bondia, Varilly - On asymptotic expansions of twisted products.pdf},
         pages = {2789--2796},
         slaccitation = {\%\%CITATION = JMAPA,30,2789\\;\%\%},
         title = {{On Asymptotic expansions of twisted products}},
         volume = {30},
         year = {1989}
 }
 
 @book{Jackson:1962,
         author = {J. D. Jackson},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Jackson J.D. Classical electrodynamics (Wiley, 1962)(T)(656s).djvu},
         title = {{Classical Electrodynamics}},
         year = {1962}
 }
 
 @misc{Kasprzak:2010,
         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.},
         author = {P. Kasprzak},
         keywords = {Operator Algebras (math.OA)},
         localfile = {2010 - Kasprzak - Rieffel deformation of group coactions.pdf},
         month = jun,
         pdf = {http://arxiv.org/pdf/1006.3416},
         title = {{Rieffel deformation of group coactions}},
         url = {http://arxiv.org/abs/1006.3416},
         v1descr = {Thu, 17 Jun 2010 10:12:06 GMT (18kb)},
         year = {2010}
 }
 
 @book{Borchers:1996-1,
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{H.-J.}}}}}}}}}}}}}}}}}}}}}}}}} Borchers},
         localfile = {http://theory.djvu},
         publisher = {Springer},
         title = {{Translation Group and Particle Representations in Quantum Field Theory}},
         year = {1996}
 }
 
 @article{ChuMadoreSteinacker:2001,
         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''.},
         author = {{{{{{{{{{{{{{{{{{{{{{{{{{C.-S.}}}}}}}}}}}}}}}}}}}}}}}}} Chu and J. Madore and H. Steinacker},
         journal = {JHEP},
         keywords = {High Energy Physics - Theory (hep-th)},
         localfile = {2001 - Chu, Madore, Steinacker - Scaling Limits of the Fuzzy Sphere at one Loop.pdf},
         pages = {038},
         pdf = {http://arxiv.org/pdf/hep-th/0106205},
         title = {{Scaling Limits of the Fuzzy Sphere at one Loop}},
         url = {http://arxiv.org/abs/hep-th/0106205},
         v1descr = {Fri, 22 Jun 2001 11:38:21 GMT (16kb)},
         v1url = {http://www.arxiv.org/abs/hep-th/0106205v1},
         v2descr = {Tue, 21 Aug 2001 20:31:29 GMT (17kb)},
         volume = {0108},
         year = {2001}
 }
 
 @article{Rieffel:2002,
         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.},
         author = {M. A. Rieffel},
         keywords = {High Energy Physics - Theory (hep-th); Metric Geometry (math.MG); Operator Algebras (math.OA); Quantum Physics (quant-ph); Representation Theory (math.RT)},
         localfile = {2001 - Rieffel - Matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance.pdf},
         month = dec,
         pdf = {http://arxiv.org/pdf/math/0108005},
         title = {{Matrix algebras converge to the sphere for quantum Gromov--Hausdorff distance}},
         url = {http://arxiv.org/abs/math/0108005},
         v1descr = {Wed, 1 Aug 2001 19:08:16 GMT (25kb)},
         v1url = {http://www.arxiv.org/abs/math/0108005v1},
         v2descr = {Thu, 12 Dec 2002 19:58:42 GMT (26kb)},
         year = {2002}
 }
 
 @article{DybalskiTanimoto:2010,
         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.},
         author = {W. Dybalski and Y. Tanimoto},
         journal = {Preprint},
         keywords = {High Energy Physics - Theory (hep-th); kw:warping; Mathematical Physics (math-ph)},
         localfile = {2010 - Dybalski, Tanimoto - Asymptotic completeness in a class of massless relativistic quantum field theories.pdf},
         month = jun,
         pdf = {http://arxiv.org/pdf/1006.5430},
         title = {{Asymptotic completeness in a class of massless relativistic quantum field theories }},
         url = {http://arxiv.org/abs/1006.5430},
         v1descr = {Mon, 28 Jun 2010 18:34:55 GMT (16kb)},
         year = {2010}
 }
 
 @article{FrohlichOsterwalderSeiler:1983,
         author = {J. Fr{\"{o}}hlich and K. Osterwalder and E. Seiler},
         journal = {Annals Math.},
         keywords = {kw:NC-Wick},
         localfile = {1983 - Fr\"{o}hlich, Osterwalder, Seiler - On Virtual representations of symmetric spaces and their analytic continuation.pdf},
         pages = {461--489},
         slaccitation = {\%\%CITATION = ANMAA,118,461\\;\%\%},
         title = {{On Virtual representations of symmetric spaces and their analytic continuation}},
         url = {http://www.jstor.org/stable/2006979},
         volume = {118},
         x-color = {#19ffd1},
         year = {1983}
 }
 
 @book{Helgason:1962,
         author = {S. Helgason},
         localfile = {http://spaces.djvu},
         publisher = {Academic Press},
         title = {{Differential Geometry and Symmetric Spaces}},
         year = {1962}
 }
 
 @article{Seiler:1982,
         author = {E. Seiler},
         journal = {Lect. Notes Phys.},
         keywords = {kw:NC-Wick},
         localfile = {http://mechanics.djvu},
         pages = {1--192},
         slaccitation = {\%\%CITATION = LNPHA,159,1\\;\%\%},
         title = {{Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics}},
         volume = {159},
         year = {1982}
 }
 
 @misc{AcharyyaVaidya:2010,
         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.},
         author = {N. Acharyya and S. Vaidya},
         keywords = {General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)},
         localfile = {2010 - Acharyya, Vaidya - Uniformly Accelerated Observer in Moyal Spacetime.pdf},
         month = jun,
         pdf = {http://arxiv.org/pdf/1005.4666},
         title = {{Uniformly Accelerated Observer in Moyal Spacetime}},
         url = {http://arxiv.org/abs/1005.4666},
         v1descr = {Tue, 25 May 2010 19:25:19 GMT (21kb)},
         v1url = {http://www.arxiv.org/abs/1005.4666v1},
         v2descr = {Wed, 2 Jun 2010 15:17:03 GMT (21kb)},
         v2url = {http://www.arxiv.org/abs/1005.4666v2},
         v3descr = {Mon, 7 Jun 2010 14:18:59 GMT (21kb)},
         year = {2010}
 }
 
 @book{Kirillov:2004,
         author = {A.A. Kirillov},
         keywords = {kw:UDF},
         localfile = {/home/gandalf/Physik/Fachb\"{u}cher/Kirillov - Lectures on the Orbit Method.pdf},
         publisher = {American Mathematical Society},
         title = {{Lectures on the Orbit Method}},
         year = {2004}
 }
 
 @misc{BieliavskyGurauRivasseau:2008,
         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.},
         author = {P. Bieliavsky and R. Gurau and V. Rivasseau},
         keywords = {High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Symplectic Geometry (math.SG); kw:UDF},
         localfile = {2008 - Bieliavsky, Gurau, Rivasseau - Non Commutative Field Theory on Rank One Symmetric Spaces.pdf},
         month = jun,
         pdf = {http://arxiv.org/pdf/0806.4255},
         title = {{Non Commutative Field Theory on Rank One Symmetric Spaces}},
         url = {http://arxiv.org/abs/0806.4255},
         v1descr = {Thu, 26 Jun 2008 18:33:06 GMT (26kb)},
         year = {2008}
 }
 
 @article{CushmanKallen:2006,
         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.},
         author = {R. Cushman and W. van der Kallen},
         journal = {Acta Appl Math},
         keywords = {kw:UDF; Representation Theory (math.RT)},
         localfile = {2006 - Cushman, van der Kallen - Adjoint and Coadjoint Orbits of the Poincare Group.pdf},
         pages = {65--89},
         pdf = {http://arxiv.org/pdf/math/0305442},
         title = {{Adjoint and coadjoint orbits of the Poincar\'{e} group}},