Uniform Semiclassical Approximation for the Wigner $6j$ Symbol in Terms of Rotation Matrices

Details Uniform Semiclassical Approximation for the Wigner $6j$ Symbol in Terms of Rotation Matrices Uniform Semiclassical Approximation for the Wigner $6j$ Symbol in Terms of Rotation Matrices

2009-05-26

arxiv.org/abs/0905.4240v2

Physics

Mathematical Physics

44 pages plus 20 figures

Scientific paper

A new uniform asymptotic approximation for the Wigner $6j$ symbol is given in terms of Wigner rotation matrices ($d$-matrices). The approximation is uniform in the sense that it applies for all values of the quantum numbers, even those near caustics. The derivation of the new approximation is not given, but the geometrical ideas supporting it are discussed and numerical tests are presented, including comparisons with the exact $6j$-symbol and with the Ponzano-Regge approximation.

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