{
  "id": "math/0402313",
  "version": "v2",
  "published": "2004-02-19T17:13:55.000Z",
  "updated": "2004-11-17T20:10:18.000Z",
  "title": "Geometric quantization, complex structures and the coherent state transform",
  "authors": [
    "Carlos Florentino",
    "Pedro Matias",
    "Jose Mourao",
    "Joao P. Nunes"
  ],
  "comment": "to appear in Journal of Functional Analysis",
  "categories": [
    "math.DG",
    "hep-th",
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "It is shown that the heat operator in the Hall coherent state transform for a compact Lie group $K$ is related with a Hermitian connection associated to a natural one-parameter family of complex structures on $T^*K$. The unitary parallel transport of this connection establishes the equivalence of (geometric) quantizations of $T^*K$ for different choices of complex structures within the given family. In particular, these results establish a link between coherent state transforms for Lie groups and results of Hitchin and Axelrod, Della Pietra and Witten.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-11-17T20:10:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81S10",
      "53D50",
      "22E30"
    ],
    "keywords": [
      "complex structures",
      "geometric quantization",
      "hall coherent state transform",
      "compact lie group",
      "unitary parallel transport"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 644850,
      "adsabs": "2004math......2313F"
    }
  }
}