Regularization of the Hamiltonian constraint and the closure of the constraint algebra

Details Regularization of the Hamiltonian constraint and the closure of the constraint algebra Regularization of the Hamiltonian constraint and the closure of the constraint algebra

1994-11-15

arxiv.org/abs/gr-qc/9411038v1

Phys.Rev. D55 (1997) 2059-2068

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, epsfig.sty

Scientific paper

10.1103/PhysRevD.55.2059

In the paper we discuss the process of regularization of the Hamiltonian constraint in the Ashtekar approach to quantizing gravity. We show in detail the calculation of the action of the regulated Hamiltonian constraint on Wilson loops. An important issue considered in the paper is the closure of the constraint algebra. The main result we obtain is that the Poisson bracket between the regulated Hamiltonian constraint and the Diffeomorphism constraint is equal to a sum of regulated Hamiltonian constraints with appropriately redefined regulating functions.

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