Gauge-Invariant Differential Renormalization: Abelian Case

TL;DR

This paper introduces a gauge-invariant differential renormalization method for Abelian theories, preserving gauge symmetry at all orders and simplifying calculations like the ABJ anomaly, especially in four-dimensional contexts.

Contribution

The paper develops a new gauge-invariant differential renormalization technique applicable in coordinate and momentum space, enhancing calculations in theories with chiral and supersymmetries.

Findings

Gauge invariance preserved to all orders in Abelian case.

Simplifies calculation of ABJ triangle anomaly.

Applicable in four-dimensional theories with chiral and supersymmetries.

Abstract

A new version of differential renormalization is presented. It is based on pulling out certain differential operators and introducing a logarithmic dependence into diagrams. It can be defined either in coordinate or momentum space, the latter being more flexible for treating tadpoles and diagrams where insertion of counterterms generates tadpoles. Within this version, gauge invariance is automatically preserved to all orders in Abelian case. Since differential renormalization is a strictly four-dimensional renormalization scheme it looks preferable for application in each situation when dimensional renormalization meets difficulties, especially, in theories with chiral and super symmetries. The calculation of the ABJ triangle anomaly is given as an example to demonstrate simplicity of calculations within the presented version of differential renormalization.