On the constraint algebra of quantum gravity in the loop representation

Abstract

Although an important issue in canonical quantization, the problem of representing the constraint algebra in the loop representation of quantum gravity has received little attention. The only explicit computation was performed by Gambini, Garat and Pullin for a formal point-splitting regularization of the diffeomorphism and Hamiltonian constraints. It is shown that the calculation of the algebra simplifies considerably when the constraints are expressed not in terms of generic area derivatives but rather as the specific shift operators that reflect the geometric meaning of the constraints.

17 pages, LaTeX, 2 figures included with epsf

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Cited by in corpus (5)

• ``Sum over Surfaces'' form of Loop Quantum Gravity
• Loop constraints: A habitat and their algebra
• The constraint algebra in Smolins' $G\to 0$ limit of 4d Euclidean Gravity
• Regularization of the Hamiltonian constraint and the closure of the constraint algebra
• Vassiliev invariants: a new framework for quantum gravity