Additional considerations in the definition and renormalization of non-covariant gauges

TL;DR

This paper explores the complexities of defining and renormalizing non-covariant gauges, specifically axial gauge, highlighting the constraints imposed by residual gauge invariance on renormalization prescriptions.

Contribution

It analyzes the restrictions on renormalization in non-covariant gauges, providing conditions and solutions for the prescription-term to maintain consistency with WT identities.

Findings

Renormalization prescriptions must satisfy non-trivial conditions.

Residual gauge invariance imposes additional constraints.

A restricted class of solutions to these conditions is identified.

Abstract

In this work, we pursue further consequences of a general formalism for non-covariant gauges developed in an earlier work (hep-th/0205042). We carry out further analysis of the additional restrictions on renormalizations noted in that work. We use the example of the axial gauge A_3=0. We find that if multiplicative renormalization together with ghost-decoupling is to hold, the ``prescription-term'' (that defines a prescription) cannot be chosen arbitrarily but has to satisfy certain non-trivial conditions (over and above those implied by the validity of power counting) arising from the WT identities associated with the residual gauge invariance. We also give a restricted class of solutions to these conditions.