{
  "id": "1007.0798",
  "version": "v1",
  "published": "2010-07-06T02:44:43.000Z",
  "updated": "2010-07-06T02:44:43.000Z",
  "title": "Coherent States on Hilbert Modules",
  "authors": [
    "S. Twareque Ali",
    "T. Bhattacharyya",
    "S. Shyam Roy"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over $C^*$-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert $C^*$-modules which have a natural left action from another $C^*$-algebra say, $\\mathcal A$. The coherent states are well defined in this case and they behave well with respect to the left action by $\\mathcal A$. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive kernel between two $C^*$-algebras, in complete analogy to the Hilbert space situation. Related to this there is a dilation result for positive operator valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-06T02:44:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81S99"
    ],
    "keywords": [
      "coherent states",
      "hilbert modules",
      "natural left action",
      "hilbert space situation",
      "natural settings"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/44/27/275202",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2011,
      "month": "Jul",
      "volume": 44,
      "number": 27,
      "pages": 275202
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JPhA...44A5202T"
    }
  }
}