Interacting Quantum Fields on a Curved Background

TL;DR

This paper develops a method for perturbatively analyzing interacting quantum fields in curved spacetime using microlocal analysis and the Epstein-Glaser approach, advancing quantum field theory in gravitational backgrounds.

Contribution

It adapts the Epstein-Glaser renormalization method to curved spacetime, utilizing microlocal analysis and wave front set techniques for Hadamard states.

Findings

Successfully extends perturbative quantum field theory to curved backgrounds.

Provides a rigorous framework for renormalization on globally hyperbolic spacetimes.

Utilizes microlocal analysis to characterize quantum states via wave front sets.

Abstract

A renormalized perturbative expansion of interacting quantum fields on a globally hyperbolic spacetime is performed by adapting the Bogoliubov Epstein Glaser method to a curved background. The results heavily rely on techniques from microlocal analysis, in particular on Radzikowski's characterization of Hadamard states by wave front sets of Wightman functions.