Maximal Non-Abelian Gauges and Topology of Gauge Orbit Space

Details Maximal Non-Abelian Gauges and Topology of Gauge Orbit Space Maximal Non-Abelian Gauges and Topology of Gauge Orbit Space

1998-12-18

arxiv.org/abs/hep-th/9812174v1

Nucl.Phys. B551 (1999) 399-424

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, harvmac, 1 figure

Scientific paper

10.1016/S0550-3213(99)00228-X

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 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 not 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 fields 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 behaviour 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.

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