{
  "id": "quant-ph/0604118",
  "version": "v2",
  "published": "2006-04-17T12:47:13.000Z",
  "updated": "2006-08-09T11:59:39.000Z",
  "title": "Lorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator",
  "authors": [
    "C. Quesne",
    "V. M. Tkachuk"
  ],
  "comment": "20 pages, no figure, some very small changes, published version",
  "journal": "J.Phys.A39:10909-10922,2006",
  "doi": "10.1088/0305-4470/39/34/021",
  "categories": [
    "quant-ph",
    "hep-th",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "The $D$-dimensional $(\\beta, \\beta')$-two-parameter deformed algebra introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-dimensional quantized space-time. In the D=3 and $\\beta=0$ case, the latter reproduces Snyder algebra. The deformed Poincar\\'e transformations leaving the algebra invariant are identified. It is shown that there exists a nonzero minimal uncertainty in position (minimal length). The Dirac oscillator in a 1+1-dimensional space-time described by such an algebra is studied in the case where $\\beta'=0$. Extending supersymmetric quantum mechanical and shape-invariance methods to energy-dependent Hamiltonians provides exact bound-state energies and wavefunctions. Physically acceptable states exist for $\\beta < 1/(m^2 c^2)$. A new interesting outcome is that, in contrast with the conventional Dirac oscillator, the energy spectrum is bounded.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-08-09T11:59:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11.30.Cp",
      "03.65.Fd",
      "03.65.Pm",
      "03.65.Ge",
      "11.30.Pb"
    ],
    "keywords": [
      "lorentz-covariant deformed algebra",
      "minimal length",
      "application",
      "exact bound-state energies",
      "nonzero minimal uncertainty"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 714930
    }
  }
}