Constraining differential renormalization in abelian gauge theories

TL;DR

This paper introduces a differential renormalization method for abelian gauge theories at one loop that maintains gauge invariance and simplifies the renormalization process by avoiding extraneous constants.

Contribution

It proposes a new procedure for differential renormalization that preserves gauge invariance and reduces the need for additional renormalization constants in abelian theories.

Findings

Method preserves abelian gauge invariance automatically.

Amplitudes are expressed using a basis of singular functions.

Consistency with the propagator equation determines local terms.

Abstract

We present a procedure of differential renormalization at the one loop level which avoids introducing unnecessary renormalization constants and automatically preserves abelian gauge invariance. The amplitudes are expressed in terms of a basis of singular functions. The local terms appearing in the renormalization of these functions are determined by requiring consistency with the propagator equation. Previous results in abelian theories, with and without supersymmetry, are discussed in this context.