Improved Epstein-Glaser Renormalization II. Lorentz invariant framework

TL;DR

This paper extends Epstein-Glaser renormalization to a Lorentz invariant framework, simplifying counterterms in Minkowski space and improving the BPHZL method for massless theories.

Contribution

It introduces a Lorentz invariant T-renormalization method that simplifies counterterms and enhances the BPHZL approach in massless quantum field theories.

Findings

Lorentz invariant T-renormalization relates to causal Riesz distributions.

A covariant subtraction rule in momentum space is established.

The method simplifies counterterms needed for Lorentz invariance in Minkowski space.

Abstract

The Epstein--Glaser type T-subtraction introduced by one of the authors in a previous paper is extended to the Lorentz invariant framework. The advantage of using our subtraction instead of Epstein and Glaser's standard W-subtraction method is especially important when working in Minkowski space, as then the counterterms necessary to keep Lorentz invariance are simplified. We show how T-renormalization of primitive diagrams in the Lorentz invariant framework directly relates to causal Riesz distributions. A covariant subtraction rule in momentum space is found, sharply improving upon the BPHZL method for massless theories.