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Existence of local covariant time ordered products of quantum fields in curved spacetime. (English) Zbl 1015.81043
Summary: We establish the existence of local, covariant time ordered products of local Wick polynomials for a free scalar field in curved spacetime. Our time ordered products satisfy all of the hypotheses of our previous uniqueness theorem, so our construction essentially completes the analysis of the existence, uniqueness, and renormalizability of the perturbative expansion for nonlinear quantum field theories in curved spacetime. As a byproduct of our analysis, we derive a scaling expansion of the time ordered products about the total diagonal that expresses them as a sum of products of polynomials in the curvature times Lorentz invariant distributions, plus a remainder term of arbitrarily low scaling degree [see also V. Moretti, ibid. 232, 189-221 (2003; Zbl 1015.81042)].

81T20 Quantum field theory on curved space or space-time backgrounds
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
46N50 Applications of functional analysis in quantum physics
81T05 Axiomatic quantum field theory; operator algebras
83C47 Methods of quantum field theory in general relativity and gravitational theory
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