Gauge fields out of equilibrium: A gauge invariant formulation and the Coulomb gauge

We study the Abelian Higgs model out of equilibrium in two different approaches: a gauge invariant formulation proposed by Boyanovsky et al. and in the Coulomb gauge. We show that both approaches become equivalent in a consistent one loop approximation. Furthermore, we carry out a proper renormalization for the model in order to prepare the equations for a numerical implementation. The additional degrees of freedom, which arise in gauge theories, influence the behavior of the system dramatically. A comparison with results in the ’t Hooft–Feynman background gauge found by us recently shows very good agreement.