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.