Maximal non-abelian gauges and topology of gauge orbit space

Abstract

We introduce two maximal non-abelian gauge fixing conditions on the space of gauge orbits M for gauge theories over spaces with dimensions d ⩽ 3. The gauge fixings are complete in the sense that they describe an open dense set M 0 of the space of gauge orbits M and select one and only one gauge field per gauge orbit in M 0. There are no Gribov copies or ambiguities in these gauges. M 0 is a contractible manifold with trivial topology. The set of gauge orbits which are not described by the gauge conditions M / M 0 is the boundary of M 0 and encodes all non-trivial topological properties of the space of gauge orbits. The gauge field configurations of this boundary M / M 0 can be explicitly identified with non-abelian monopoles and they are shown to play a very relevant role in the non-perturbative behavior of gauge theories in one, two and three space dimensions. It is conjectured that their role is also crucial for quark confinement in 3+1-dimensional gauge theories.