Spontaneous symmetry breakdown in massless scalar electrodynamics and a Brans-Dicke-type gravitational theory

The dynamical symmetry breaking through the Coleman-Weinberg phenomenon is examined in massless scalar electrodynamics and in a Brans-Dicke-type gravitational theory. The calculation of the effective potential is reformulated using the background-field method and dimensional regularization. Similarity between the two theories is stressed. For the case of the gravitational theory, a relation between the Higgs scalar mass and the gravitational constant is obtained. All one-loop counter-terms for the matterless Brans-Dicke theory are explicitly obtained and the problem of renormalizability is examined. (orig.)