{
  "id": "1104.3641",
  "version": "v1",
  "published": "2011-04-19T05:25:03.000Z",
  "updated": "2011-04-19T05:25:03.000Z",
  "title": "Asymptotic Limits of the Wigner $15J$-Symbol with Small Quantum Numbers",
  "authors": [
    "Liang Yu"
  ],
  "comment": "13 pages, 8 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present new asymptotic formulas for the Wigner $15j$-symbol with two, three, or four small quantum numbers, and provide numerical evidence of their validity. These formulas are of the WKB form and are of a similar nature as the Ponzano-Regge formula for the Wigner $6j$-symbol. They are expressed in terms of edge lengths and angles of geometrical figures associated with angular momentum vectors. In particular, the formulas for the $15j$-symbol with two, three, and four small quantum numbers are based on the geometric figures of the $9j$-, $6j$-, and $3j$-symbols, respectively, The geometric nature of these new asymptotic formulas pave the way for further analysis of the semiclassical limits of vertex amplitudes in loop quantum gravity models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-19T05:25:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "small quantum numbers",
      "asymptotic limits",
      "loop quantum gravity models",
      "angular momentum vectors",
      "asymptotic formulas pave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 896904,
      "adsabs": "2011arXiv1104.3641Y"
    }
  }
}