Landau gauge Jacobian and BRST symmetry

TL;DR

This paper introduces a novel approach to gauge-fixing in Yang-Mills theories using a generalized Faddeev-Popov method that involves a different Jacobian and an extended BRST symmetry.

Contribution

It presents a new gauge-fixing procedure as a change of variables with a modified Jacobian and extends the BRST symmetry beyond the standard formulation.

Findings

The Jacobian is the modulus of the standard Faddeev-Popov determinant.

The gauge-fixing Lagrangian density is local and has an extended BRST symmetry.

The approach generalizes the standard Landau gauge fixing method.

Abstract

We propose a generalisation of the Faddeev-Popov trick for Yang-Mills fields in the Landau gauge. The gauge-fixing is achieved as a genuine change of variables. In particular the Jacobian that appears is the modulus of the standard Faddeev-Popov determinant. We give a path integral representation of this in terms of auxiliary bosonic and Grassman fields extended beyond the usual set for standard Landau gauge BRST. The gauge-fixing Lagrangian density appearing in this context is local and enjoys a new extended BRST and anti-BRST symmetry though the gauge-fixing Lagrangian density in this case is not BRST exact.