A geometric look at the lattice Gribov problem, and some copy free smooth gauges

We have studied gauge fixing via the standard local extremization algorithm for 2-dimensional U(1). On a lattice with spherical topology S2 where all copies are lattice artifacts, we find that the number of these 'Gribov' copies diverges in the continuum limit. On a torus, we show that lattice artifacts can lead to the wrong evaluation of the gauge-invariant correlation length, when measured via a gauge-fixed procedure; this bias does not disappear in the continuum limit. We then present a global approach, based on geometric decomposition of the gauge field, which produces unique smooth gauge fixed fields. (orig.)