Considerations about Gribov ambiguities for the abelian Higgs model in the presence of chemical potential and temperature

In this letter we discuss the influence of a U(1) chemical potential $\mu$ on the existence of Gribov copies in a U(1) theory at finite temperature $T$. We show that the chemical potential conspires against the existence of Gribov copies in the sense that it restricts the space of solutions of the consistency equation for the gauge parameter. Explicit solutions are found for T=0, as function of $\mu$. In the finite temperature case we find also a class of solutions which satisfy the KMS boundary conditions in the euclidean time direction, having also a vanishing behavior when $|\mathbf r|\to\infty$