REGULARIZATION OF THE HAMILTONIAN CONSTRAINT AND THE CLOSURE OF THE CONSTRAINT ALGEBRA

Authors
Citation
R. Borissov, REGULARIZATION OF THE HAMILTONIAN CONSTRAINT AND THE CLOSURE OF THE CONSTRAINT ALGEBRA, Physical review. D. Particles and fields, 55(4), 1997, pp. 2059-2068
Citations number
22
Categorie Soggetti
Physics, Particles & Fields
ISSN journal
05562821
Volume
55
Issue
4
Year of publication
1997
Pages
2059 - 2068
Database
ISI
SICI code
0556-2821(1997)55:4<2059:ROTHCA>2.0.ZU;2-A
Abstract
In canonical quantum gravity regularization is needed to define the op erator products occurring in the calculations. We examine the backgrou nd dependence of the action of the regulated Hamiltonian constraint on the quantum states in the Ashtekar approach, and investigate whether the regularization preserves the closure of the constraint algebra. We compute the action on states based on smooth loops, on loops with int ersections, and on loops with kinks. The results in all these cases de pend on the arbitrary metric used in the calculations. We also show th at the regularization does not affect the closure of the constraint al gebra: The commutator of the regulated Hamiltonian constraint with the gauge and the diffeomorphism constraints equals zero and a linear com bination of Hamiltonian constrains, respectively. On the other hand, t he simple point-splitting regularization does not make the commutator of two Hamiltonian constraints expressible as a combination of constra ints.