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

الأصل · EN

The structure of the moduli spaces:= / of (all, not just flat) SL(2,C) and SU(1,1) connections on a n-manifold is analysed. For any topology on the corresponding spaces of all connections which satisfies the weak requirement of compatibility with the affine structure of, the moduli space 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. 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 4 and 3 dimensions.