1994/11/15 by Roumen Borissov
Mathematics · Medicine · Physics and Astronomy · #Algebra over a field #Algebra representation #Black Holes and Theoretical Physics #Cellular algebra #Commutator #Computer science #Constraint algebra #Diffeomorphism #First class constraint #Hamiltonian (control theory) #Hamiltonian constraint #Lie conformal algebra #Loop quantum gravity #Mathematical optimization #Mathematical physics #Mathematics #Moment map #Neuroblastoma Research and Treatments #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Regularization (linguistics) #Wheeler–DeWitt equation #gr-qc
paper · pdf · doi:10.1103/physrevd.55.2059
published as Phys.Rev. D55 (1997) 2059-2068 · 23 pages, epsfig.sty
arxiv created 1994/11/15 · openalex publication_date 1997/02/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In canonical quantum gravity regularization is needed to define the operator products occurring in the calculations. We examine the background 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 intersections, and on loops with kinks. The results in all these cases depend on the arbitrary metric used in the calculations. We also show that the regularization does not affect the closure of the constraint algebra: The commutator of the regulated Hamiltonian constraint with the gauge and the diffeomorphism constraints equals zero and a linear combination of Hamiltonian constrains, respectively. On the other hand, the simple point-splitting regularization does not make the commutator of two Hamiltonian constraints expressible as a combination of constraints.