Gauge Independence of the Effective Potential Revisited

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.Comment: 13 pages, no figures, Latex, final version published in NP