Lorentz gauge and Gribov ambiguity in the compact lattice U(1) theory

The Gribov ambiguity problem is studied for compact U(1) lattice theory within the Lorentz gauge. In the Coulomb phase, it is shown that apart from double Dirac sheets all gauge (i.e. Gribov) copies originate mainly from the zero-momentum modes of the gauge fields. The removal of the zero-momentum modes turns out to be necessary for reaching the absolute maximum of the gauge functional $F(\theta )$. A new gauge fixing procedure - zero-momentum Lorentz gauge - is proposed.