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We study the abelian Higgs model out-of-equilibrium in two differentapproaches, a gauge invariant formulation, proposed by Boyanovsky et al.\cite{Boyanovsky:1996dc} and in the Coulomb gauge. We show that both approachesbecome equivalent in a consistent one loop approximation. Furthermore, we carryout a proper renormalization for the model in order to prepare the equationsfor a numerical implementation. The additional degrees of freedom, which arisein gauge theories, influence the behavior of the system dramatically. Acomparison with results in the 't Hooft-Feynman background gauge found by usrecently, shows very good agreement.Comment: 32 pages, 8 figure

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