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

TL;DR

This paper develops a local microlocal analysis-based renormalization method for constructing interacting quantum field theories on curved spacetimes, enabling precise definitions of local observables and Wick polynomials.

Contribution

It introduces a purely local renormalization approach using microlocal analysis, extending the Epstein-Glaser method to curved backgrounds and defining local operator algebras.

Findings

Constructed local algebras of observables on curved spacetimes

Provided a new definition of Wick polynomials as operator-valued distributions

Developed a general method for extending distributions across surfaces

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.