ELECTROWEAK MAGNETISM: THEORY AND APPLICATIONS

Abstract

The classical electroweak theory is unstable for magnetic fields H satisfying [Formula: see text], mw being the W mass. We discuss the origin of this instability and the peculiar anti-screening property of the W-condensate formed. The anti-screening is closely related to the asymptotic freedom of the SU (2)w-fields. Assuming that the Higgs mass mh>mw there will be a restoration of SU (2)w× U y(1) symmetry for [Formula: see text]. By using Bogomol’nyi’s method in the special case where the mass of the Z-particle mz=mh we can find static magnetic solutions with a vacuum condensate of W- and Z-bosons. This class of non-perturbative solutions interpolate between the constant magnetic field in the broken phase [Formula: see text] and a constant U y(1) field in the symmetric phase [Formula: see text]. The consequences of this magnetic instability are discussed in the cases of superconducting cosmic strings, high temperatures (the early universe) and high energy collisions.