1994/06/22 by Cayetano Di Bartolo, C. Di Bartolo, Rodolfo Gambini +3 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Computer science #Cosmology and Gravitation Theories #Diffeomorphism #Hamiltonian (control theory) #Hamiltonian constraint #Irreducible representation #Loop (graph theory) #Loop quantum gravity #Mathematical optimization #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Real representation #Regularization (linguistics) #Representation (politics) #Spin foam #Spin network #Wheeler–DeWitt equation #gr-qc
paper · pdf · doi:10.1103/physrevd.51.502
published as Phys.Rev. D51 (1995) 502-516 · 27 pages, report IFFC/94-13
arxiv created 1994/06/22 · openalex publication_date 1995/01/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A new representation of quantum gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group that we call the extended loop group behaves locally as an infinite dimensional Lie group. Quantum gravity can be realized on the state space of extended loop-dependent wave functions. The extended representation generalizes the loop representation and contains this representation as a particular case. The resulting diffeomorphism and Hamiltonian constraints take a very simple form and allow us to apply functional methods and simplify the loop calculus. In particular we show that the constraints are linear in the momenta. The nondegenerate solutions known in the loop representation are also solutions of the constraints in the new representation. An approach to the regularization problems associated with the formal calculus is performed. We show that the solutions are generalized knot invariants, smooth in the extended variables, and any framing is unnecessary.