{
  "id": "2204.12842",
  "version": "v1",
  "published": "2022-04-27T11:01:01.000Z",
  "updated": "2022-04-27T11:01:01.000Z",
  "title": "$2$-Spinors via Linear Algebra",
  "authors": [
    "Roger Plymen"
  ],
  "comment": "14 pages",
  "categories": [
    "math-ph",
    "gr-qc",
    "math.MP"
  ],
  "abstract": "We give a streamlined account of $2$-spinors, up to and including the Dirac equation, using little more than the resources of linear algebra. We prove that the Dirac bundle is isomorphic to the associated bundles $\\mathrm{SL}_2(\\mathbb{C}) \\times_{\\mathrm{SU}_2} S$ and $\\mathrm{SL}_2(\\mathbb{C}) \\times_{\\mathrm{SU}_2} \\bar{S}$. A solution of the Dirac equation determines a pair of conjugate $2$-spinor fields over the mass shell $X_m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-27T11:01:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear algebra",
      "dirac equation determines",
      "dirac bundle",
      "mass shell",
      "spinor fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}