Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1993-11-07
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
42 pages, To be published in ``Knots and Quantum Gravity'' (ed. J.Baez, Oxford U.Press)
Scientific paper
Integral calculus on the space of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well--suited for quantization of diffeomorphism invariant theories of connections. The general setting is provided by the abelian C* algebra of functions on the quotient space of connections generated by Wilson loops (i.e., by the traces of holonomies of connections around closed loops). The representation theory of this algebra leads to an interesting and powerful ``duality'' between gauge--equivalence classes of connections and certain equivalence classes of closed loops. In particular, regular measures on (a suitable completion of) connections/gauges are in 1--1 correspondence with certain functions of loops and diffeomorphism invariant measures correspond to (generalized) knot and link invariants. By carrying out a non--linear extension of the theory of cylindrical measures on topological vector spaces, a faithful, diffeomorphism invariant measure is introduced. This measure can be used to define the Hilbert space of quantum states in theories of connections. The Wilson--loop functionals then serve as the configuration operators in the quantum theory.
Ashtekar Abhay
Lewandowski Jerzy
No associations
LandOfFree
Representation Theory of Analytic Holonomy C* Algebras 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 Representation Theory of Analytic Holonomy C* Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representation Theory of Analytic Holonomy C* Algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-258469