Maximal Abelian gauge and a generalized BRST transformation

TL;DR

This paper demonstrates how a finite field-dependent BRST transformation connects the gauge-fixed SU(2) Yang-Mills theories in Lorenz and Maximal Abelian gauges, providing insights into Abelian dominance.

Contribution

It introduces a generalized FFBRST approach to relate different gauge-fixed formulations of SU(2) Yang-Mills theory, highlighting the role of Jacobian contributions.

Findings

FFBRST transformation links Lorenz and MA gauges

Jacobian accounts for gauge transformation effects

Potential insights into Abelian dominance

Abstract

We apply a generalized Becchi-Rouet-Stora-Tyutin (BRST) formulation to establish a connection between the gauge-fixed $SU(2)$ Yang-Mills (YM) theories formulated in the Lorenz gauge and in the Maximal Abelian (MA) gauge. It is shown that the generating functional corresponding to the Faddeev-Popov (FP) effective action in the MA gauge can be obtained from that in the Lorenz gauge by carrying out an appropriate finite and field-dependent BRST (FFBRST) transformation. In this procedure, the FP effective action in the MA gauge is found from that in the Lorenz gauge by incorporating the contribution of non-trivial Jacobian due to the FFBRST transformation of the path integral measure. The present FFBRST formulation might be useful to see how Abelian dominance in the MA gauge is realized in the Lorenz gauge.