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Journal Article

On the constraint algebra of quantum gravity in the loop representation


Brügmann,  Bernd
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Brügmann, B. (1996). On the constraint algebra of quantum gravity in the loop representation. Nuclear Physics B, 474(1), 249-268.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-5B6B-4
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.