Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds

Details Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds

1999-03-12

arxiv.org/abs/math-ph/9903028v1

Commun.Math.Phys.208:623-661,2000

Physics

Mathematical Physics

38 pages, LaTeX with AMSLaTeX style option, Micro.tex macrofile

Scientific paper

10.1007/s002200050004

We present a perturbative construction of interacting quantum field theories on any smooth globally hyperbolic manifold. We develop a purely local version of the Stueckelberg-Bogoliubov-Epstein-Glaser method of renormalization using techniques from microlocal analysis. As byproducts, we describe a perturbative construction of local algebras of observables, present a new definition of Wick polynomials as operator-valued distributions on a natural domain, and we find a general method for the extension of distributions which were defined on the complement of some surfaces.

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