Abstract
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 ⩾ T c and varies continuously to nonzero values for temperatures below T c, implying the existence of a second-order phase transition.
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