{
  "id": "1104.1499",
  "version": "v3",
  "published": "2011-04-08T07:00:33.000Z",
  "updated": "2011-05-12T16:59:52.000Z",
  "title": "Semiclassical Analysis of the Wigner $9J$-Symbol with Small and Large Angular Momenta",
  "authors": [
    "Liang Yu",
    "Robert G. Littlejohn"
  ],
  "comment": "18 pages, 16 figures. To appear in Phys. Rev. A",
  "journal": "Phys. Rev. A83: 052114,2011",
  "doi": "10.1103/PhysRevA.83.052114",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We derive a new asymptotic formula for the Wigner $9j$-symbol, in the limit of one small and eight large angular momenta, using a novel gauge-invariant factorization for the asymptotic solution of a set of coupled wave equations. Our factorization eliminates the geometric phases completely, using gauge-invariant non-canonical coordinates, parallel transports of spinors, and quantum rotation matrices. Our derivation generalizes to higher $3nj$-symbols. We display without proof some new asymptotic formulas for the $12j$-symbol and the $15j$-symbol in the appendices. This work contributes a new asymptotic formula of the Wigner $9j$-symbol to the quantum theory of angular momentum, and serves as an example of a new general method for deriving asymptotic formulas for $3nj$-symbols.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-05-12T16:59:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Vf",
      "03.65.Sq",
      "02.30.Ik"
    ],
    "keywords": [
      "angular momentum",
      "large angular momenta",
      "asymptotic formula",
      "semiclassical analysis",
      "novel gauge-invariant factorization"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review A",
      "year": 2011,
      "month": "May",
      "volume": 83,
      "number": 5,
      "pages": "052114"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 895891,
      "adsabs": "2011PhRvA..83e2114Y"
    }
  }
}