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Representation Theory of Analytic Holonomy C* Algebras
Abhay Ashtekar, Jerzy Lewandowski
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 f…
Completeness of Wilson loop functionals on the moduli space of and -connections
Abhay Ashtekar, Jerzy Lewandowski
The structure of the moduli spaces $\M := \A/\G$ of (all, not just flat) and connections on a n-manifold is analysed. For any topology on the corresponding spac…
Minisuperspaces: Observables and Quantization
Abhay Ashtekar, Ranjeet S. Tate, Claes Uggla
A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new can…
Mathematical Problems of Non-perturbative Quantum General Relativity
Abhay Ashtekar
The purpose of these lectures is to discuss in some detail a new, non-perturbative approach to quantum gravity. I would like to present the basic ideas, outline the key results tha…