ON THE FINITE-TEMPERATURE EFFECTIVE POTENTIAL IN SCALAR QED WITH N-FLAVORS

The effective potential of scalar quantum electrodynamics with N flavors of complex scalar fields is studied, by performing a self-consistent 1/N expansion up to next to leading order in 1/N. Starting from the broken phase at zero temperature, the theory exhibits a phase transition to the symmetric phase at some finite temperature T(c). We work in general covariant gauges and demonstrate the gauge invariance of both, the critical temperature T(c) and the minimization condition at any finite temperature T. Furthermore, the only minimum of the potential is at zero scalar vacuum expectation value for any temperature T greater-than-or-equal-to T(c) and varies continuously to nonzero values for temperatures below T(c), implying the existence of a second-order phase transition.