Split Dimensional Regularization for the Coulomb Gauge

TL;DR

This paper introduces split dimensional regularization, a novel method for handling Feynman integrals in Coulomb gauge Yang-Mills theory, ensuring consistency and applicability to both Abelian and non-Abelian models.

Contribution

It proposes a new regularization technique for Coulomb gauge Yang-Mills theory that is internally consistent and ambiguity-free.

Findings

Yields a nontransverse, local one-loop Yang-Mills self-energy.

Demonstrates necessity of ghosts to satisfy Ward/BRS identities.

Applicable to both Abelian and non-Abelian gauge theories.

Abstract

A new procedure for regularizing Feynman integrals in the noncovariant Coulomb gauge is proposed for Yang-Mills theory. The procedure is based on a variant of dimensional regularization, called split dimensional regularization, which leads to internally consistent, ambiguity-free integrals. It is demonstrated that split dimensional regularization yields a one-loop Yang-Mills self-energy that is nontransverse, but local. Despite the noncovariant nature of the Coulomb gauge, ghosts are necessary in order to satisfy the appropriate Ward/BRS identity. The computed Coulomb-gauge Feynman integrals are applicable to both Abelian and non-Abelian gauge models. PACS: 11.15, 12.38.C