Landau gauge Jacobian and BRST symmetry

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 Grassmann 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.