The space of states of quantum gravity in terms of loops and extended loops: some remarks

Abstract

This article reviews the status of several solutions to all the constraints of quantum gravity that have been proposed in terms of loops and extended loops. We discuss pitfalls of several of the results and in particular discuss the issues of covariance and regularization of the constraints in terms of extended loops. We also propose a formalism for ``thickened out loops'' which does not face the covariance problems of extended loops and may allow to regularize expressions in a consistent manner.

16 Pages, Revtex/epsf, one figure included.

References in corpus (9)

• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• The physical hamiltonian in nonperturbative quantum gravity
• How the Jones Polynomial Gives Rise to Physical States of Quantum General Relativity
• The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space
• The Extended Loop Representation of Quantum Gravity
• Loop Representations for 2+1 Gravity on a Torus
• Loop Variable Inequalities in Gravity and Gauge Theory
• Regularization of the Hamiltonian constraint and the closure of the constraint algebra
• Recent Mathematical Developments in Quantum General Relativity

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