UNITARY GAUGE AND PHASE-TRANSITION AT FINITE TEMPERATURE

The unitary gauge in perturbative calculations of the phase transitions at finite temperature by Landau's method is investigated. The leading high-temperature contribution of the two-loop effective potential of the abelian Higgs model in unitary gauge is explicitly calculated. We find that already in the two-loop approximation appears a non-analyticity in the symmetry breaking parameter which makes a significant contribution in the high-temperature asymptotics of the effective potential near the phase-transition point. This fact justifies the remarks made in the literature, which suggest that the critical temperature should be calculated from the leading high-temperature contribution of the one-loop effective potential only in renormalizable gauges. As an additional inadequacy of the unitary gauge to investigate the phase transition at finite temperature, it is also shown that in this approximation the temperature-dependent divergences are not cancelled, contrary to what occurs for renormalizable gauges.