Possible resolution of the lattice Gribov ambiguity

The Gribov ambiguity in lattice gauge theory is discussed. The Landau gauge and the finite-temperature temporal gauge (${\mathrm{\partial }}_4$ ${\mathit{A}}_4$=0) are formulated as maximization conditions on the lattice. This formulation is shown to eliminate Gribov copies from the temporal gauge. The possibility that it also eliminates copies from the Landau gauge is discussed. An algorithm which will eliminate Gribov copies from the lattice implementation of the Landau gauge, in case any remain, is introduced and studied via Monte Carlo simulation. The algorithm involves a noncovariant intermediate step and so eliminates the copies at the cost of the possible introduction of a violation of lattice Poincaré symmetry. The covariance of this algorithm is studied numerically and no evidence is found for symmetry violation, which indicates that either the maximization form of the lattice Landau gauge is free of copies, or that the modified algorithm selects one in an acceptably covariant way.