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arXiv · 0912.5384

Asymptotics of the Wigner 9j symbol

Hal M. Haggard·Robert G. Littlejohn
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Abstract

We present the asymptotic formula for the Wigner 9j-symbol, valid when all quantum numbers are large, in the classically allowed region. As in the Ponzano-Regge formula for the 6j-symbol, the action is expressed in terms of lengths of edges and dihedral angles of a geometrical figure, but the angles require care in definition. Rules are presented for converting spin networks into the associated geometrical figures. The amplitude is expressed as the determinant of a 2x2 matrix of Poisson brackets. The 9j-symbol possesses caustics associated with the fold and elliptic and hyperbolic umbilic catastrophes. The asymptotic formula obeys the exact symmetries of the 9j-symbol.

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Hal M. Haggard, Robert G. Littlejohn. 2009-12-29. Asymptotics of the Wigner 9j symbol. https://doi.org/10.1088/0264-9381%2F27%2F13%2F135010

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