Uniform Approximation from Symbol Calculus on a Spherical Phase Space

Details Uniform Approximation from Symbol Calculus on a Spherical Phase Space Uniform Approximation from Symbol Calculus on a Spherical Phase Space

2011-05-21

arxiv.org/abs/1105.4220v2

J. Phys. A: Math. Theor. 44 505202 (2011)

Physics

Mathematical Physics

18 pages, 5 figures

Scientific paper

10.1088/1751-8113/44/50/505202

We use symbol correspondence and quantum normal form theory to develop a more general method for finding uniform asymptotic approximations. We then apply this method to derive a result we announced in an earlier paper, namely, the uniform approximation of the $6j$-symbol in terms of the rotation matrices. The derivation is based on the Stratonovich-Weyl symbol correspondence between matrix operators and functions on a spherical phase space. The resulting approximation depends on a canonical, or area preserving, map between two pairs of intersecting level sets on the spherical phase space.

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