# Generating series and asymptotics of classical spin networks

Francesco Costantino; Julien Marché

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 10, page 2417-2452
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topCostantino, Francesco, and Marché, Julien. "Generating series and asymptotics of classical spin networks." Journal of the European Mathematical Society 017.10 (2015): 2417-2452. <http://eudml.org/doc/277226>.

@article{Costantino2015,

abstract = {We study classical spin networks with group SU$_2$. In the first part, using Gaussian integrals, we compute their generating series in the case where the edges are equipped with holonomies; this generalizes Westbury’s formula. In the second part, we use an integral formula for the square of the spin network and perform stationary phase approximation under some non-degeneracy hypothesis. This gives a precise asymptotic behavior when the labels are rescaled by a constant going to infinity.},

author = {Costantino, Francesco, Marché, Julien},

journal = {Journal of the European Mathematical Society},

keywords = {spin networks; generating series; asymptotical behavior; saddle point method; coherent states; spin networks; generating series; asymptotical behavior; saddle point method; coherent states},

language = {eng},

number = {10},

pages = {2417-2452},

publisher = {European Mathematical Society Publishing House},

title = {Generating series and asymptotics of classical spin networks},

url = {http://eudml.org/doc/277226},

volume = {017},

year = {2015},

}

TY - JOUR

AU - Costantino, Francesco

AU - Marché, Julien

TI - Generating series and asymptotics of classical spin networks

JO - Journal of the European Mathematical Society

PY - 2015

PB - European Mathematical Society Publishing House

VL - 017

IS - 10

SP - 2417

EP - 2452

AB - We study classical spin networks with group SU$_2$. In the first part, using Gaussian integrals, we compute their generating series in the case where the edges are equipped with holonomies; this generalizes Westbury’s formula. In the second part, we use an integral formula for the square of the spin network and perform stationary phase approximation under some non-degeneracy hypothesis. This gives a precise asymptotic behavior when the labels are rescaled by a constant going to infinity.

LA - eng

KW - spin networks; generating series; asymptotical behavior; saddle point method; coherent states; spin networks; generating series; asymptotical behavior; saddle point method; coherent states

UR - http://eudml.org/doc/277226

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.