2011

Semiclassical Analysis of the Wigner $9J$-Symbol with Small and Large Angular Momenta

Yu, Liang, Littlejohn, Robert G.

Understand

We derive a new asymptotic formula for the Wigner $9j$-symbol, in the limit of one small and eight large angular momenta, using a novel gauge-invariant factorization for the asymptotic solution of a set of coupled wave equations.

Our factorization eliminates the geometric phases completely, using gauge-invariant non-canonical coordinates, parallel transports of spinors, and quantum rotation matrices.
Our derivation generalizes to higher $3nj$-symbols.
We display without proof some new asymptotic formulas for the $12j$-symbol and the $15j$-symbol in the appendices.

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