On the Gribov Problem for Generalized Connections
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The bundle structure of the space \(\) of Ashtekar's generalized connections is investigated in the compact case. It is proven that every stratum is a locally trivial fibre bundle. The only stratum being a principal fibre bundle is the generic stratum. Its structure group equals the space \(\) of all generalized gauge transforms modulo the constant center-valued gauge transforms. For abelian gauge theories the generic stratum is globally trivial and equals the total space \(\). However, for a certain class of non-abelian gauge theories – e.g., all SU(N) theories – the generic stratum is nontrivial. This means, there are no global gauge fixings – the so-called Gribov problem. Nevertheless, for many physical measures there is a covering of the generic stratum by trivializations each having total measure 1. Finally, possible physical consequences and the relation between fundamental modular domains and Gribov horizons are discussed.
KeywordsGauge Theory Fibre Bundle Total Space Abelian Gauge Bundle Structure
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