  The effective equations of motion for low-frequency mean gauge fields in the
Abelian Higgs model are investigated in the presence of a scalar condensate,
near the high temperature equilibrium. We determine the current induced by an
inhomogeneous background gauge field in the linear response approximation up to
order $e^4$, assuming adiabatic variation of the scalar fields. The physical
degrees of freedom are found and a physical gauge choice for the numerical
study of the combined Higgs+gauge evolution is proposed.
