Vilkovisky-DeWitt Effective Potential Revisited in Gauge-Free Framework

TL;DR

This paper revisits the Vilkovisky-DeWitt effective potential within a gauge-free framework, resolving gauge dependence issues in scalar QED and demonstrating the necessity of combining both methods for reparametrization invariance.

Contribution

It introduces a gauge-free approach to scalar QED and shows how combining it with Vilkovisky-DeWitt formalism achieves reparametrization invariance of the effective potential.

Findings

Gauge-free approach removes gauge dependence of the effective potential.

The gauge-free result differs from the standard Vilkovisky-DeWitt result.

Combining gauge-free and Vilkovisky-DeWitt methods ensures reparametrization invariance.

Abstract

An alternative approach to scalar quantum electrodynamics has been proposed where the usual gauge redundancy of the theory do not manifest. The gauge-dependence of Coleman- Weinberg effective potential is resolved using gauge-free approach leading to a unique scalar to vector mass ratio. The gauge-free result is compared with the one obtained in Vilkovisky-DeWitt geometric framework and it is shown that it differs from the standard result reported earlier. It is also shown that for reparametrization invariance of the Coleman-Weinberg potential one must combine the Vilkovisky-DeWitt method with the gauge-free approach.