Completeness of Wilson loop functionals on the moduli space of SL(2,C) and SU(1,1) connections

A. Ashtekar, J. Lewandowski

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Abstract

The structure of the moduli spaces M:=A/G of (all, not just flat) SL(2,C) and SU(1,1) connections on an n-manifold is analysed. For any topology of the corresponding spaces A of all connections which satisfies the weak requirement of compatibility with the affine structure of A, the moduli space M is shown to be non-Hausdorff. It is then shown that the Wilson loop functionals-i.e. the traces of holonomies of connections around closed loops-are complete in the sense that they suffice to separate all separable points of M. The methods are general enough to allow the underlying n-manifold to be topologically non-trivial and for connections to be defined on non-trivial bundles. The results have implications for canonical quantum general relativity in four and three dimensions.

Original languageEnglish (US)
Article number002
Pages (from-to)L69-L74
JournalClassical and Quantum Gravity
Volume10
Issue number6
DOIs
StatePublished - Dec 1 1993

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

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