{
  "id": "math-ph/0006019",
  "version": "v1",
  "published": "2000-06-17T09:25:22.000Z",
  "updated": "2000-06-17T09:25:22.000Z",
  "title": "A tensor interpretation of the 2D Dirac equation",
  "authors": [
    "Dmitri Vassiliev"
  ],
  "comment": "11 pages, LaTeX",
  "categories": [
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "We consider the Dirac equation in flat Minkowski 3-space and rewrite it as the Maxwell equation in Minkowski 4-space with torsion. The torsion tensor is defined as the dual of the electromagnetic vector potential. Our model clearly distinguishes the electron and the positron without resorting to \"negative frequencies\": we produce a real scalar invariant (charge) which indicates whether we are looking at an electron or a positron. Another interesting feature of our model is that the free electron and positron are identified with gradient type solutions of the standard (torsion free) Maxwell equation; such solutions have traditionally been disregarded on the grounds of gauge invariance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-06-17T09:25:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81T99",
      "53A99"
    ],
    "keywords": [
      "2d dirac equation",
      "tensor interpretation",
      "maxwell equation",
      "real scalar invariant",
      "electromagnetic vector potential"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.ph...6019V"
    }
  }
}