Gauge invariance and the effective potential

The gauge invariance of physical quantities calculated in spontaneously broken gauge theories using the effective potential is discussed. The basic mechanism by which gauge invariance is guaranteed was discovered by Nielsen, and involves identifies of Ward-Takahashi type. The main purpose of the present paper is to supplement Nielsen's formal work by explicit and complete calculations at the one loop level. The Abelian Higgs model is the simplest available, but it has to consider in general R/sub zeta/ gauges in order to avoid infrared divergence. A full derivation of the appropriate Nielsen identities in such gauges is given. Certain restrictions on the class of allowed R/sub zeta/ gauges are found, which resolve some difficulties in the use of such gauges in effective potential calculations. The one-loop calculations are performed using Jackiw's functional method. Explicit forms are obtained for the effective propagators required by Jackiw's formalism, for our generalized R/sub t/ gauges; the model may therefore provide a useful laboratory for other investigations. The extension of the identities to spontanteously broken non-Abelian gauge theory is given