{
  "id": "quant-ph/0109086",
  "version": "v2",
  "published": "2001-09-18T16:25:25.000Z",
  "updated": "2001-11-26T20:12:28.000Z",
  "title": "Coherent states on spheres",
  "authors": [
    "Brian C. Hall",
    "Jeffrey J. Mitchell"
  ],
  "comment": "Revised version. Submitted to J. Mathematical Physics",
  "journal": "J.Math.Phys. 43 (2002) 1211-1236; Erratum-ibid. 46 (2005) 059901",
  "doi": "10.1063/1.1446664",
  "categories": [
    "quant-ph",
    "gr-qc",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated phase space T*(S^d). These coherent states are NOT of Perelomov type but rather are constructed as the eigenvectors of suitably defined annihilation operators. We describe as well the Segal-Bargmann representation for the system, the associated unitary Segal-Bargmann transform, and a natural inversion formula. Although many of these results are in principle special cases of the results of B. Hall and M. Stenzel, we give here a substantially different description based on ideas of T. Thiemann and of K. Kowalski and J. Rembielinski. All of these results can be generalized to a system whose configuration space is an arbitrary compact symmetric space. We focus on the sphere case in order to be able to carry out the calculations in a self-contained and explicit way.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-11-26T20:12:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Ge",
      "03.65.Db",
      "02.30.Uu"
    ],
    "keywords": [
      "coherent states",
      "arbitrary compact symmetric space",
      "natural inversion formula",
      "principle special cases",
      "associated unitary segal-bargmann transform"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 2002,
      "month": "Mar",
      "volume": 43,
      "number": 3,
      "pages": 1211
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 564075,
      "adsabs": "2002JMP....43.1211H"
    }
  }
}