{
  "id": "0905.1217",
  "version": "v1",
  "published": "2009-05-08T09:46:34.000Z",
  "updated": "2009-05-08T09:46:34.000Z",
  "title": "Structure, classifcation, and conformal symmetry, of elementary particles over non-archimedean space-time",
  "authors": [
    "V. S. Varadarajan",
    "J. Virtanen"
  ],
  "journal": "Lett.Math.Phys.89:171-182,2009",
  "doi": "10.1007/s11005-009-0351-2",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "It is known that no length or time measurements are possible in sub-Planckian regions of spacetime. The Volovich hypothesis postulates that the micro-geometry of spacetime may therefore be assumed to be non-archimedean. In this letter, the consequences of this hypothesis for the structure, classification, and conformal symmetry of elementary particles, when spacetime is a flat space over a non-archimedean field such as the $p$-adic numbers, is explored. Both the Poincar\\'e and Galilean groups are treated. The results are based on a new variant of the Mackey machine for projective unitary representations of semidirect product groups which are locally compact and second countable. Conformal spacetime is constructed over $p$-adic fields and the impossibility of conformal symmetry of massive and eventually massive particles is proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-08T09:46:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conformal symmetry",
      "elementary particles",
      "non-archimedean space-time",
      "classifcation",
      "semidirect product groups"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Letters in Mathematical Physics",
      "year": 2009,
      "month": "Sep",
      "pages": 38
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 819769,
      "adsabs": "2009LMaPh.tmp...38V"
    }
  }
}