A note on BRST quantization of SU(2) Yang-Mills mechanics

TL;DR

This paper examines the BRST quantization of SU(2) Yang-Mills mechanics in reduced dimensions, highlighting gauge-specific issues and proposing solutions involving additional ghost variables.

Contribution

It identifies gauge-dependent problems in BRST quantization of SU(2) Yang-Mills mechanics and introduces singlet ghost variables to address these issues.

Findings

BRST quantization faces difficulties in the unitary gauge

Introducing singlet ghost variables resolves gauge-related problems

Lorenz gauge allows consistent BRST quantization without extra issues

Abstract

The quantization of SU(2) Yang-Mills theory reduced to 0+1 space-time dimensions is performed in the BRST framework. We show that in the unitary gauge $A_0 = 0$ the BRST procedure has difficulties which can be solved by introduction of additional singlet ghost variables. In the Lorenz gauge $\dot{A}_0 = 0$ one has additional unphysical degrees of freedom, but the BRST quantization is free of the problems in the unitary gauge.