{
  "id": "0806.4682",
  "version": "v5",
  "published": "2008-06-30T18:37:05.000Z",
  "updated": "2008-11-19T16:47:40.000Z",
  "title": "The classical point-electron in Colombeau's theory of nonlinear generalized functions",
  "authors": [
    "Andre Gsponer"
  ],
  "comment": "30 pages. Final published version with a few minor corrections",
  "journal": "J. Math. Phys., Vol.49 (2008) 102901 (22 pages)",
  "doi": "10.1063/1.2982236",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The electric and magnetic fields of a pole-dipole singularity attributed to a point-electron-singularity in the Maxwell field are expressed in a Colombeau algebra of generalized functions. This enables one to calculate dynamical quantities quadratic in the fields which are otherwise mathematically ill-defined: The self-energy (i.e., `mass'), the self-angular momentum (i.e., `spin'), the self-momentum (i.e., `hidden momentum'), and the self-force. While the total self-force and self-momentum are zero, therefore insuring that the electron-singularity is stable, the mass and the spin are diverging integrals of delta-squared-functions. Yet, after renormalization according to standard prescriptions, the expressions for mass and spin are consistent with quantum theory, including the requirement of a gyromagnetic ratio greater than one. The most striking result, however, is that the electric and magnetic fields differ from the classical monopolar and dipolar fields by delta-function terms which are usually considered as insignificant, while in a Colombeau algebra these terms are precisely the sources of the mechanical mass and spin of the electron-singularity.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2008-11-19T16:47:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear generalized functions",
      "colombeaus theory",
      "classical point-electron",
      "colombeau algebra",
      "magnetic fields differ"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 2008,
      "month": "Oct",
      "volume": 49,
      "number": 10,
      "pages": 102901
    },
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JMP....49j2901G"
    }
  }
}