## Geometry & Topology

### Asymptotics of classical spin networks

#### 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.

#### Article information

Source
Geom. Topol., Volume 17, Number 1 (2013), 1-37.

Dates
Revised: 9 May 2012
Accepted: 12 July 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732514

Digital Object Identifier
doi:10.2140/gt.2013.17.1

Mathematical Reviews number (MathSciNet)
MR3035322

Zentralblatt MATH identifier
1277.57020

#### Citation

Garoufalidis, Stavros; van der Veen, Roland. Asymptotics of classical spin networks. Geom. Topol. 17 (2013), no. 1, 1--37. doi:10.2140/gt.2013.17.1. https://projecteuclid.org/euclid.gt/1513732514

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