Gauge Independence of the Effective Potential Revisited

TL;DR

This paper revisits the gauge independence of the effective potential in spontaneously broken gauge theories using extended BRS symmetry, deriving Nielsen identities that confirm gauge independence without constraints on gauge-fixing parameters.

Contribution

It introduces a formalism with Grassmann parameters for gauge dependence analysis, providing a quick derivation of Nielsen identities valid across a broad class of gauges.

Findings

Nielsen identities hold without constraints on gauge-fixing parameters.

The formalism confirms gauge independence of the effective potential.

Results are scheme-independent due to algebraic renormalization.

Abstract

We apply the formalism of extended BRS symmetry to the investigation of the gauge dependence of the effective potential in a spontaneously symmetry broken gauge theory. This formalism, which includes a set of Grassmann parameters defined as the BRS variations of the gauge-fixing parameters, allows us to derive in a quick and unambiguous way the related Nielsen identities, which express the physical gauge independence, in a class of generalized 't Hooft gauges, of the effective potential. We show in particular that the validity of the Nielsen identities does not require any constraint on the gauge-fixing parameters, to the contrary of some claims found in the literature. We use the method of algebraic renormalization, which leads to results independent of the particular renormalization scheme used.