Gauge-free Coleman-Weinberg Potential

Abstract: The gauge-dependence of the one loop Coleman-Weinberg effective potential in scalar electrodynamics is resolved using a gauge-free approach not requiring any gauge-fixing of quantum fluctuations of the photon degrees of freedom. This leads to a unique dynamical ratio at one loop of the Higgs mass to the photon mass. We compare our approach and results with those obtained in geometric framework of DeWitt and Vilkovisky, which maintains invariance under field redefinitions as well as invariance under background gauge transformations, but {\it requires}, in contrast to our approach, gauge fixing of {\it fluctuating} photon fields. We also discuss possible modifications of the Coleman-Weinberg potential if we adapt the DeWitt-Vilkovisky method to our gauge-free approach for scalar QED.