Interacting Quantum Fields in Curved Space: Renormalizability of $\varphi^4$

TL;DR

This paper develops a perturbative approach to construct the $$ quantum field theory on curved space-times, adapting renormalization techniques to handle the complexities introduced by curvature.

Contribution

It introduces a novel adaptation of the Epstein and Glaser renormalization method for curved space-times using microlocal analysis, establishing renormalizability of the $$ model.

Findings

Successful construction of the $$ model on curved space-times.

Extension of renormalization techniques to curved backgrounds.

Framework for analyzing quantum fields in curved geometries.

Abstract

We present a perturbative construction of the $\varphi^4$ model on a smooth globally hyperbolic space-time. Our method relies on a adaptation of the Epstein and Glaser method of renormalization to curved space-times using techniques from microlocal analysis.