On the Gribov Problem for Generalized Connections
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Submission date: 08. Jul. 2000
published in: Communications in mathematical physics, 234 (2003) 3, p. 423-454
DOI number (of the published article): 10.1007/s00220-002-0745-9
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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, there is a covering of the generic stratum by trivializations each having total induced Haar measure 1.