Asymptotics of classical spin networks : Appendix by Don Zagier

Garoufalidis, Stavros; van der Veen, Roland

doi:10.2140/gt.2013.17.1

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Asymptotics of classical spin networks : Appendix by Don Zagier

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Zagier, Don
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.2140/gt.2013.17.1
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arXiv:0902.3113.pdf
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Garoufalidis, S., & van der Veen, R. (2013). Asymptotics of classical spin networks: Appendix by Don Zagier. Geometry & Topology, 17(1), 28-33. doi:10.2140/gt.2013.17.1.

Cite as: https://hdl.handle.net/21.11116/0000-0006-B554-F

Abstract

A spin network is a cubic ribbon graph labeled by representations of
$\mathrm{SU}(2)$. 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 non-rigorous guess of its Stokes constants), in the appendix.