1996/01/07 by Jorge Griego · 7 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Configuration space #Diffeomorphism #Hamiltonian (control theory) #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Loop (graph theory) #Loop quantum gravity #Loop space #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Propagator #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Representation (politics) #Theoretical physics #Wave function #gr-qc
paper · pdf · doi:10.1016/0550-3213(96)00235-0
published in Nuclear Physics B 473(1-2), 291-307 (Elsevier BV) · 19 pages
arxiv created 1996/01/07 · openalex publication_date 1996/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In the loop representation the quantum constraints of gravity can be solved. This fact allowed significant progress in the understanding of the space of states of the theory. The analysis of the constraints over loop dependent wavefunctions has been traditionally based upon geometric (in contrast to analytic) properties of the loops. The reason for this preferred way is twofold: for one hand the inherent difficulties associated with the analytic loop calculus, and on the other our limited knowledge about the analytic properties of knots invariants. Extended loops provide a way to overcome the difficulties at both levels. For one hand, a systematic method to construct analytic expressions of diffeomorphism invariants (the extended knots) in terms of the Chern-Simons propagators can be developed. Extended knots are simply related to ordinary knots (at least formally). The analytic expressions of knot invariants could be produced then in a generic way. On the other hand, the evaluation of the Hamiltonian over extended loop wavefunctions can be thoroughly accomplished in the extended loop framework. These two ingredients promote extended loops as a potential resort for answering important questions about quantum gravity.