Generating series and asymptotics of classical spin networks

Details Generating series and asymptotics of classical spin networks Generating series and asymptotics of classical spin networks

2011-03-29

arxiv.org/abs/1103.5644v2

Mathematics

Geometric Topology

33 pages, 3 figures; in version 2 added one reference and a comment on the hypotheses of Theorem 1.3

Scientific paper

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 networks 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.

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