Generating series and asymptotics of classical spin networks

Understand

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.