Configuration Space BPHZ Renormalization on Analytic Spacetimes

TL;DR

This paper develops a configuration space approach to BPHZ renormalization within perturbative algebraic quantum field theory, extending its applicability to analytic spacetimes and connecting it with momentum space methods.

Contribution

It introduces a configuration space version of BPHZ renormalization applicable to analytic spacetimes, bridging it with momentum space techniques.

Findings

Established a configuration space BPHZ renormalization framework.

Extended the method's applicability to analytic spacetimes.

Analyzed the limit of constant coupling in this context.

Abstract

A configuration space version of BPHZ renormalization is proved in the realm of perturbative algebraic quantum field theory. All arguments are formulated entirely in configuration space so that the range of application is extended to analytic spacetimes. Further the relation to the momentum space method is established. In the course of that, it is necessary to study the limit of constant coupling.