On the Gribov Problem for Generalized Connections
Abstract
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 centervalued gauge transforms. For abelian gauge theories the generic stratum is globally trivial and equals the total space . However, for a certain class of nonabelian gauge theories  e.g., all SU(N) theories  the generic stratum is nontrivial. This means, there are no global gauge fixings  the socalled 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2003
 DOI:
 10.1007/s0022000207459
 arXiv:
 arXiv:mathph/0007001
 Bibcode:
 2003CMaPh.234..423F
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 81T13 (Primary) 53C05;
 55R10;
 57R22;
 58D19 (Secondary)
 EPrint:
 38 pages, LaTeX, v2: main results unchanged, but article widely restructured