{
  "id": "1202.0886",
  "version": "v2",
  "published": "2012-02-04T09:58:34.000Z",
  "updated": "2012-08-16T16:17:12.000Z",
  "title": "Quantization of (volume-preserving) actions on R^d",
  "authors": [
    "Benoit Dherin",
    "Igor Mencattini"
  ],
  "comment": "21 pages. We added the notion of formal G-systems, associated with formal quantizations of smooth actions, and proved a corresponding existence and rigidity result",
  "categories": [
    "math-ph",
    "math.MP",
    "math.RT"
  ],
  "abstract": "We associate a space of (formal) representations on the space of h-formal power series with coefficients in the space of smooth functions on Rd (which we call quantizations) with an action of a group on Rd by smooth diffeomorphisms. If the action is further volume preserving, these quantizations can be realized as unitary representations on square summable functions on Rd by bounded h-dependent Fourier integral operators, the formal case corresponding to the asymptotics in the limit h going to zero. We construct DGAs controlling these quantizations and prove existence and rigidity results for them.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-16T16:17:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantization",
      "bounded h-dependent fourier integral operators",
      "h-formal power series",
      "unitary representations",
      "square summable functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.0886D"
    }
  }
}