Abstract
Rovelli and Smolin (1989) have developed a non-perturbative quantisation of canonical gravity based on the Ashtekar variables (1988) in terms of which the constraints of canonical quantum gravity become polynomials. The author proposes alternative loop variables which are not invariant under the discrete transformations which cause the problems for the Rovelli-Smolin observables and yet which still form a closed Poisson bracket algebra. The author first discusses the case of (2+1)-gravity and then defines similar variables for complexified (3+1)-gravity. Expressions are obtained for the diffeomorphism and Hamiltonian constraints in terms of the new loop variables and the author gives an interpretation of them within the framework of the differential geometry of both the loop space, and the space of SL(2, C) connections, of the spatial three manifold.
Published Version
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