2011/03/29 by Francesco Costantino, Costantino, Francesco, Julien Marche +1
Mathematics · Physics and Astronomy · #57Mxx (Primary) #81R05 (Secondary) #83C27 #83C45 #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.GT #math.MP #math.QA #msc:57Mxx #msc:81R05 #msc:83C27 #msc:83C45
paper · pdf · doi:10.48550/arxiv.1103.5644
33 pages, 3 figures; in version 2 added one reference and a comment on the hypotheses of Theorem 1.3
arxiv created 2011/05/01 · arxiv updated 2011/05/03
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.