On the Gribov Problem for Generalized Connections

Abstract

The bundle structure of the space $\Ab$ 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 $\Gb$ 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 $\Ab$. 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.

38 pages, LaTeX, v2: main results unchanged, but article widely restructured; extended introduction; new sect. 7.1 and app. F (replacing former sect. 7); new discussion; new prop. C.1 + G.1; refs. added

References in corpus (3)

• Relation between polymer and Fock excitations
• Constructing Hamiltonian quantum theories from path integrals in a diffeomorphism invariant context
• Hyphs and the Ashtekar-Lewandowski Measure

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