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

Romeo Brunetti·Klaus Fredenhagen
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Abstract

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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Romeo Brunetti, Klaus Fredenhagen. 1999-03-12. Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds. https://doi.org/10.1007/s002200050004

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