On the Gribov Problem for Generalized Connections
نویسنده
چکیده
The bundle structure of the space A 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 G 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 A. 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
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