Generating series and asymptotics of classical spin networks

  • Francesco Costantino

    Université Paul Sabatier, Toulouse, France
  • Julien Marché

    École Polytechnique, Palaiseau, France


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. 2417–2452

DOI 10.4171/JEMS/561