标题： Wigner$12J$符号在庞扎诺-雷吉相位中的渐近极限 显示英文标题

标题： Asymptotic Limits of the Wigner $12J$-Symbol in Terms of the Ponzano-Regge Phases

摘要： 对于具有一个较小和11个较大角动量的$12j$符号，有两种渐近公式。 我们之前在[L. Yu, Phys. Rev. A84 022101 (2011)]中推导出了第一种公式。 本文我们将推导第二种公式。 我们发现，这种$12j$符号的第二种渐近公式是用与两个$6j$符号相关的矢量图表示的，即两个共享一个公共面的相邻四面体的矢量图。 因此，渐近公式中出现了两组Ponzano-Regge相位。 这项工作为角动量的再耦合理论贡献了另一种Wigner$12j$符号的渐近公式。 显示英文摘要

摘要： There are two types of asymptotic formulas for the $12j$ symbol with one small and 11 large angular momenta. We have derived the first type of formula previously in [L. Yu, Phys. Rev. A84 022101 (2011)]. We will derive the second type in this paper. We find that this second asymptotic formula for the $12j$ symbol is expressed in terms of the vector diagram associated with two $6j$ symbols, namely, the vector diagram of two adjacent tetrahedra sharing a common face. As a result, two sets of Ponzano-Regge phases appear in the asymptotic formula. This work contributes another asymptotic formula of the Wigner $12j$ symbol to the re-coupling theory of angular momenta.