1994/04/28 by Rodolfo Gambini, Alcides Garat, Jorge Pullin · 2 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebra representation #Cellular algebra #Combinatorics #Constraint (computer-aided design) #Constraint algebra #Geometry #Loop (graph theory) #Loop quantum cosmology #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum Mechanics and Applications #Quantum gravity #Quantum mechanics #Representation (politics) #Spin foam #Theoretical physics #gr-qc
paper · pdf · doi:10.1142/s0218271895000417
published as Int.J.Mod.Phys. D4 (1995) 589-616 · 18 pages, Revtex, no figures, CGPG-94/4-3
arxiv created 1994/04/28 · openalex publication_date 1995/10/01 · arxiv updated 2009/11/30 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
We study the algebra of constraints of quantum gravity in the loop representation based on Ashtekar’s new variables. We show by direct computation that the quantum commutator algebra reproduces the classical Poisson bracket one, in the limit in which regulators are removed. The calculation illustrates the use of several computational techniques for the loop representation.