Generating series and asymptotics of classical spin networks
type: Item
instance of: scholarly article
title: Generating series and asymptotics of classical spin networks
zbMATH Open document ID: 1334.57019
DOI: 10.4171/JEMS/561
author: N. E. Zubov
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2015-11-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1103.5644
review text: This paper investigates two aspects of classical spin networks with group \(SU(2)\). First, using Gaussian integrals, the paper generalizes a formula of Westbury to the case of spin networks whose edges are labeled by holonomies. A combinatorial interpretation of the formula is also provided. Second, subject to certain conditions, a formula is given for the asymptotic behaviour of the generating series of squares of spin networks as labels are rescaled by a constant diverging to infinity. Such asymptotic behaviour (proven to exist by \textit{S. Garoufalidis} and \textit{R. van der Veen} [Geom. Topol. 17, No. 1, 1--37 (2013; Zbl 1277.57020)]) is expected to recover Euclidean geometric quantities, and this type of formula is a holy grail for the study of spin networks. However, it is not known how to describe when the conditions hold for the formula and indeed no examples have been shown in which these hypotheses hold other than for the \(6j\)-symbols.
reviewed by: Daniel Moskovich
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 83C45
Mathematics Subject Classification ID: 83C27
zbMATH DE Number: 6509922
zbMATH Keywords: spin networks
zbMATH Keywords: generating series
zbMATH Keywords: asymptotical behavior
zbMATH Keywords: saddle point method
zbMATH Keywords: coherent states
MaRDI profile type: Publication
arXiv ID: 1103.5644
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description: scientific article