{
  "id": "1001.1285",
  "version": "v1",
  "published": "2010-01-08T14:43:43.000Z",
  "updated": "2010-01-08T14:43:43.000Z",
  "title": "The Hamiltonian H=xp and classification of osp(1|2) representations",
  "authors": [
    "G. Regniers",
    "J. Van der Jeugt"
  ],
  "comment": "Contribution for the Workshop Lie Theory and Its Applications in Physics VIII (Varna, 2009)",
  "journal": "AIP Conference Proceedings, vol. 1243, 138-147 (2010)",
  "doi": "10.1063/1.3460159",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The quantization of the simple one-dimensional Hamiltonian H=xp is of interest for its mathematical properties rather than for its physical relevance. In fact, the Berry-Keating conjecture speculates that a proper quantization of H=xp could yield a relation with the Riemann hypothesis. Motivated by this, we study the so-called Wigner quantization of H=xp, which relates the problem to representations of the Lie superalgebra osp(1|2). In order to know how the relevant operators act in representation spaces of osp(1|2), we study all unitary, irreducible star representations of this Lie superalgebra. Such a classification has already been made by J.W.B. Hughes, but we reexamine this classification using elementary arguments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-08T14:43:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B81",
      "81R05",
      "02.20.Sv",
      "02.30.Sa",
      "02.60.Cb"
    ],
    "keywords": [
      "classification",
      "lie superalgebra",
      "simple one-dimensional hamiltonian",
      "relevant operators act",
      "proper quantization"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "AIP Conf. Proc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010AIPC.1243..138R"
    }
  }
}