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

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

1993-04-30

arxiv.org/abs/gr-qc/9304044v1

Class.Quant.Grav.10:L69-L74,1993

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Plain TeX, 7 pages, SU-GP-93/4-?

Scientific paper

10.1088/0264-9381/10/6/002

The structure of the moduli spaces $\M := \A/\G$ 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 $\A$ 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 4 and 3 dimensions.

Affiliated with

Also associated with

No associations

Rating

Completeness of Wilson loop functionals on the moduli space of $SL(2,C)$ and $SU(1,1)$-connections does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Completeness of Wilson loop functionals on the moduli space of $SL(2,C)$ and $SU(1,1)$-connections, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Completeness of Wilson loop functionals on the moduli space of $SL(2,C)$ and $SU(1,1)$-connections will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-331690