Asymptotics of classical spin networks

Stavros Garoufalidis, Roland van der Veen

Type: Article

Publication Date: 2013-02-05

Citations: 23

DOI: https://doi.org/10.2140/gt.2013.17.1

Abstract

A spin network is a cubic ribbon graph labeled by representations of SU.2/.Spin networks are important in various areas of Mathematics (3-dimensional Quantum Topology), Physics (Angular Momentum, Classical and Quantum Gravity) and Chemistry (Atomic Spectroscopy).The evaluation of a spin network is an integer number.The main results of our paper are: (a) an existence theorem for the asymptotics of evaluations of arbitrary spin networks (using the theory of G -functions), (b) a rationality property of the generating series of all evaluations with a fixed underlying graph (using the combinatorics of the chromatic evaluation of a spin network), (c) rigorous effective computations of our results for some 6j -symbols using the Wilf-Zeilberger theory and (d) a complete analysis of the regular Cube 12j spin network (including a nonrigorous guess of its Stokes constants), in the appendix.

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