The Several Guises of the BRST Symmetry

TL;DR

This paper explores various formulations of BRST symmetry in QCD, including non-local and non-manifestly covariant forms, highlighting how different ghost variable transformations affect their properties.

Contribution

It introduces multiple forms of BRST transformations in QCD, demonstrating how changes in ghost variables influence their covariance and anticommutation relations.

Findings

BRST transformations can be expressed in non-local forms

Different ghost variable changes alter BRST and anti-BRST anticommutation

Transformations can be derived via non-standard path integral manipulations

Abstract

We present several forms in which the BRST transformations of QCD in covariant gauges can be cast. They can be non-local and even not manifestly covariant. These transformations may be obtained in the path integral formalism by non standard integrations in the ghost sector or by performing changes of ghost variables which leave the action and the path integral measure invariant. For different changes of ghost variables in the BRST and anti-BRST transformations these two transformations no longer anticommute.