We study classical spin networks with group SU. 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.
Cite this article
Francesco Costantino, Julien Marché, Generating series and asymptotics of classical spin networks. J. Eur. Math. Soc. 17 (2015), no. 10, pp. 2417–2452DOI 10.4171/JEMS/561