Chemical potentials and high temperature phase transitions in electroweak theory

The phenomena of electroweak phase transitions in the early universe depend crucially on the inclusion of the charge corresponding to the spontaneously broken symmetry, which is usually taken as classically conserved. This paper is devoted to the study of the electroweak phase transitions at high temperatures and, correspondingly, to the controversy in the literature concerning the question of the inclusion of the weak neutral charge in the standard model, for the investigation of the phase transitions of W-boson condensation and symmetry restoration in the early universe. Several arguments, general and perturbative, are given against the introduction of the weak neutral charge conservation in the nonsymmetric phase. As a consequence of the above, the W-condensation should occur even at low lepton densities and the symmetry restoration critical curve is independent of the lepton density. The use of different gauges such as the renormalizable and the unitary ones is also discussed. (orig.)