{
  "id": "1108.1881",
  "version": "v1",
  "published": "2011-08-09T08:42:48.000Z",
  "updated": "2011-08-09T08:42:48.000Z",
  "title": "Asymptotic Limits of the Wigner $12J$-Symbol in Terms of the Ponzano-Regge Phases",
  "authors": [
    "Liang Yu"
  ],
  "comment": "13 pages, 10 figures. arXiv admin note: substantial overlap with arXiv:1104.3275",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-09T08:42:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic limits",
      "vector diagram",
      "second asymptotic formula",
      "large angular momenta",
      "ponzano-regge phases appear"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 922796,
      "adsabs": "2011arXiv1108.1881Y"
    }
  }
}