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

Abstract

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.

23 pages, epsfig.sty

References in corpus (8)

• Discreteness of area and volume in quantum gravity
• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• The physical hamiltonian in nonperturbative quantum gravity
• The geometry of quantum spin networks
• Fermions in Quantum Gravity
• Integration on the space of Connections Modulo Gauge Transformations
• The constraint algebra of quantum gravity in the loop representation
• On the constraint algebra of quantum gravity in the loop representation

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• Bibliography of publications related to Classical and Quantum Gravity in terms of Connection and Loop Variables
• Closed-Flux Solutions to the Constraints for Plane Gravity Waves
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