{
  "id": "0707.2863",
  "version": "v1",
  "published": "2007-07-19T09:48:04.000Z",
  "updated": "2007-07-19T09:48:04.000Z",
  "title": "Hermite and Gegenbauer polynomials in superspace using Clifford analysis",
  "authors": [
    "Hendrik De Bie",
    "Frank Sommen"
  ],
  "comment": "18 pages, accepted for publication in J. Phys. A",
  "journal": "J.Phys.A40:10441-10456,2007",
  "doi": "10.1088/1751-8113/40/34/004",
  "categories": [
    "hep-th",
    "math.CA"
  ],
  "abstract": "The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an integration theory in superspace. Furthermore a lot of basic properties, such as orthogonality relations, differential equations and recursion formulae are proven. Finally, an interesting physical application of the super Clifford-Hermite polynomials is discussed, thus giving an interpretation to the super-dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-19T09:48:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "02.30.Gp",
      "02.30.Tb",
      "02.30.Fn"
    ],
    "keywords": [
      "superspace",
      "standard clifford analysis",
      "super clifford-hermite polynomials",
      "integration theory",
      "clifford-gegenbauer polynomials"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2007,
      "month": "Aug",
      "volume": 40,
      "number": 34,
      "pages": 10441
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 756261,
      "adsabs": "2007JPhA...4010441D"
    }
  }
}