Wigner 9 j符号的渐近性
Asymptotics of the Wigner 9j symbol
摘要：
在经典允许的区域内，我们给出了当所有量子数都很大时有效的维格纳9 j符号的渐近公式。正如在6 j符号的庞札诺-雷奇公式中，作用量是用几何图形的边长和二面角来表示的，但在定义时需要注意角度。规则的自旋网络转换成相关的几何图形。振幅表示为泊松括号的2x2矩阵的行列式。9 j符号具有与折叠、椭圆和双曲脐状灾变相关的焦散线。渐近公式服从9 j-符号的精确对称性。
英文摘要：
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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