{
  "id": "0810.5772",
  "version": "v1",
  "published": "2008-10-31T19:40:21.000Z",
  "updated": "2008-10-31T19:40:21.000Z",
  "title": "An algebraic approach to laying a ghost to rest",
  "authors": [
    "M. C. Nucci",
    "P. G. L. Leach"
  ],
  "comment": "8 pages",
  "journal": "Phys.Scripta 81:055003,2010",
  "doi": "10.1088/0031-8949/81/05/055003",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "In the recent literature there has been a resurgence of interest in the fourth-order field-theoretic model of Pais-Uhlenbeck \\cite {Pais-Uhlenbeck 50 a}, which has not had a good reception over the last half century due to the existence of {\\em ghosts} in the properties of the quantum mechanical solution. Bender and Mannheim \\cite{Bender 08 a} were successful in persuading the corresponding quantum operator to `give up the ghost'. Their success had the advantage of making the model of Pais-Uhlenbeck acceptable to the physical community and in the process added further credit to the cause of advancement of the use of ${\\cal PT} $ symmetry. We present a case for the acceptance of the Pais-Uhlenbeck model in the context of Dirac's theory by providing an Hamiltonian which is not quantum mechanically haunted. The essential point is the manner in which a fourth-order equation is rendered into a system of second-order equations. We show by means of the method of reduction of order \\cite {Nucci} that it is possible to construct an Hamiltonian which gives rise to a satisfactory quantal description without having to abandon Dirac.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-31T19:40:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic approach",
      "pais-uhlenbeck",
      "satisfactory quantal description",
      "fourth-order field-theoretic model",
      "abandon dirac"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Physica Scripta",
      "year": 2010,
      "month": "May",
      "volume": 81,
      "number": 5,
      "pages": "055003"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 801272,
      "adsabs": "2010PhyS...81e5003N"
    }
  }
}