1ST-ORDER PHASE-TRANSITIONS IN SCALAR ELECTRODYNAMICS

We investigate in detail the transition from the symmetric to the broken phase in scalar electrodynamics at finite temperature. Our analysis is based on the effective potential to order e3 and lambda3/2, where e and lambda are the gauge coupling and scalar self-coupling, respectively. Plasma masses of scalar and vector fields are determined from a set of one-loop gap equations which also yield the range in e, lambda and temperature T, where perturbation theory is consistent. We determine the values of e and lambda for which the symmetric phase is metastable. Depending on the convergence of the perturbation series, for a vector boson mass of 90 GeV the Higgs boson mass may be as large as 120 GeV. Following the theory of Langer we calculate the nucleation rate of critical droplets and determine the temperature at which a cosmological phase transition would be completed. For large vector boson and Higgs boson masses the phase transition is weakly first order.