2009/09/10 by R. Dowdall, Richard J. Dowdall, Henrique Gomes +1 · 29 citations
Mathematics · Physics and Astronomy · #Amplitude #Asymptotic analysis #Black Holes and Theoretical Physics #Boundary (topology) #Boundary value problem #Geometry #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum many-body systems #Quantum mechanics #Scaling #Scaling limit #Spins #Triangulation #gr-qc
paper · pdf · doi:10.1088/1751-8113/43/11/115203
published in Journal of Physics A Mathematical and Theoretical 43(11), 115203 (Institute of Physics) · 27 pages, multiple figures
arxiv created 2009/09/10 · openalex publication_date 2010/03/02 · arxiv updated 2012/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using the coherent state techniques developed for the analysis of the EPRL model we give the asymptotic formula for the Ponzano–Regge model amplitude for non-tardis triangulations of handlebodies in the limit of large boundary spins. The formula produces a sum over all possible immersions of the boundary triangulation and its value is given by the cosine of the Regge action evaluated on these. Furthermore the asymptotic scaling registers the existence of flexible immersions. We verify numerically that this formula approximates the 6 j -symbol for large spins.