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

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

2011-08-09

arxiv.org/abs/1108.1881v1

Physics

Mathematical Physics

13 pages, 10 figures. arXiv admin note: substantial overlap with arXiv:1104.3275

Scientific paper

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.

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