Spontaneous symmetry breaking in massless field theories: Dimensional transmutation and gauge independence

In a reformulation of the Coleman and Weinberg program, we study the parametrization of the spontaneous symmetry breaking solutions of massless field theories. Our analysis is based on a full use of the concept of the dimensional transmutation, namely the parametrization in terms of the independent invariants of the underlying renormalization group. This invariant parametrization provides a convenient setting for the operator interpretation in a given Fock space and is shown to be a powerful tool in studying general aspects of the theory beyond the one-loop approximation. In particular, the gauge independence of the physical matrix elements in the spontaneously broken solution of massless scalar electrodynamics is demonstrated to all orders in perturbation theory.