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Generating series and asymptotics of classical spin networks

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

Abstract

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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