Asymptotics of the Wigner 9j-Symbol

We present the asymptotic formula for the Wigner 9j-symbol, valid when all quantum numbers are large. The formula is a generalization of the well known asymptotic formula of Ponzano and Regge (1968) for the Wigner 6j-symbol that has played a central role in discrete approaches to 3D quantum gravity. Analysis of the classically allowed region of the 9j-symbol reveals a geometrically rich structure. We conclude with a discussion of the extension of our methods to higher 3nj-symbols. Asymptotic formulas for the higher 3nj-symbols will clarify the semiclassical limit of spinfoam approaches to quantum gravity. )