Geodesic
Generating series and asymptotics of classical spin networks
Journal of the European Mathematical Society, Tome 17 (2015) no. 10, pp. 2417-2452 Cet article a éte moissonné depuis la source EMS Press

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We study classical spin networks with group SU2​. 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.
DOI : 10.4171/jems/561
Classification : 57-XX, 81-XX, 83-XX
Keywords: Spin networks, generating series, asymptotical behavior, saddle point method, coherent states 
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     author = {Francesco Costantino and Julien March\'e},
     title = {Generating series and asymptotics of classical spin networks},
     journal = {Journal of the European Mathematical Society},
     pages = {2417--2452},
     year = {2015},
     volume = {17},
     number = {10},
     doi = {10.4171/jems/561},
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Francesco Costantino; Julien Marché. Generating series and asymptotics of classical spin networks. Journal of the European Mathematical Society, Tome 17 (2015) no. 10, pp. 2417-2452. doi: 10.4171/jems/561

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