{
  "id": "0706.3397",
  "version": "v2",
  "published": "2007-06-22T19:46:23.000Z",
  "updated": "2007-06-26T06:30:47.000Z",
  "title": "Fock representation of the renormalized higher powers of white noise and the Virasoro--Zamolodchikov--$w_{\\infty} *$--Lie algebra",
  "authors": [
    "Luigi Accardi",
    "Andreas Boukas"
  ],
  "doi": "10.1088/1751-8113/41/30/304001",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The identification of the $*$--Lie algebra of the renormalized higher powers of white noise (RHPWN) and the analytic continuation of the second quantized Virasoro--Zamolodchikov--$w_{\\infty} *$--Lie algebra of conformal field theory and high-energy physics, was recently established in \\cite{id} based on results obtained in [1] and [2]. In the present paper we show how the RHPWN Fock kernels must be truncated in order to be positive definite and we obtain a Fock representation of the two algebras. We show that the truncated renormalized higher powers of white noise (TRHPWN) Fock spaces of order $\\geq 2$ host the continuous binomial and beta processes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-06-26T06:30:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H40",
      "81S05",
      "81T30",
      "81T40"
    ],
    "keywords": [
      "lie algebra",
      "white noise",
      "fock representation",
      "conformal field theory",
      "rhpwn fock kernels"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2008,
      "month": "Aug",
      "volume": 41,
      "number": 30,
      "pages": 304001
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JPhA...41D4001A"
    }
  }
}