Abstract
The time slice axiom states that the observables which can be measured within an arbitrarily small time interval suffice to predict all other observables. While well known for free field theories where the validity of the time slice axiom is an immediate consequence of the field equation it was not known whether it also holds in generic interacting theories, the only exception being certain superrenormalizable models in 2 dimensions. In this paper we prove that the time slice axiom holds at least for scalar field theories within formal renormalized perturbation theory.
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Bär C., Ginoux N., Pfäffle F.: Wave Equations on Lorentzian Manifolds and Quantization. . RI: Amer.Math. Soc., Providence (2007)
Brunetti R., Fredenhagen K.: Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds. Commun. Math. Phys. 208, 623 (2000)
Brunetti R., Fredenhagen K., Köhler M.: The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes. Commun. Math. Phys. 180, 633–652 (1996)
Dimock J.: Algebras of Local Observables on a Manifold. Commun. Math. Phys. 77, 219–228 (1980)
Duistermaat J.J., Hörmander L.: Fourier Integral Operators II. Acta Math. 128, 183–269 (1972)
Dütsch M., Fredenhagen K.: Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion. Commun. Math. Phys. 219, 5 (2001)
Dütsch M., Fredenhagen K.: Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity. Rev. Math. Phys. 16, 1291–1348 (2004)
Epstein H., Glaser V.: The role of locality in perturbation theory. Ann Inst. H. Poincaré A 19, 211 (1973)
Fulling S.A., Narcowich F.J., Wald R.M.: Singularity structure of the two-point function in quantum field theory in curved space-time. II. Ann. Phys. (NY) 136, 243–272 (1981)
Garber W.-D.: The Connexion of Duality and Causal Properties for Generalized Free Fields. Commun. Math. Phys. 42, 195–208 (1975)
Glimm J., Jaffe A.: A \({\lambda \varphi^4}\) Quantum Field Theory without Cutoffs I. Phys. Rev. 176, 1945–1951 (1968)
Haag R.: Local Quantum Physics: Fields, particles and algebras. 2nd ed. Springer-Verlag, Berlin (1996)
Haag R., Kastler D.: An algebraic approach to field theory. J. Math. Phys. 5, 848 (1964)
Haag R., Schroer B.: Postulates of quantum field theory. J. Math. Phys. 3, 248–256 (1962)
Hollands S., Wald R.M.: Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime. Commun. Math. Phys. 223, 289–326 (2001)
Leray, J.: Hyperbolic Differential Equations. Lecture Notes, Princeton, N.J.: Institute for Advanced Study, 1963
Radzikowski M.J.: Micro-Local Approach to the Hadamard Condition in Quantum Field Theory on Curved Space-Time. Commun. Math. Phys. 179, 529–553 (1996)
Schrader R.: Yukawa Quantum Field Theory in Two Space-Time Dimensions Without Cutoffs. Ann. Phys. 70, 412–457 (1972)
Streater R.F., Wightman A.S.: PCT Spin and Statistics, and All That Reading. Addison Wesley Longman Publishing Co, MA (1989)
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Communicated by M. Salmhofer
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Chilian, B., Fredenhagen, K. The Time Slice Axiom in Perturbative Quantum Field Theory on Globally Hyperbolic Spacetimes. Commun. Math. Phys. 287, 513–522 (2009). https://doi.org/10.1007/s00220-008-0670-7
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DOI: https://doi.org/10.1007/s00220-008-0670-7