{
  "id": "math-ph/0612081",
  "version": "v2",
  "published": "2006-12-27T01:51:29.000Z",
  "updated": "2007-07-17T19:44:51.000Z",
  "title": "Left-Ideals, Dirac Fermions and SU(2)-Flavour",
  "authors": [
    "F. M. C. Witte"
  ],
  "comment": "15 pages, no figures, pdf-file",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper I reconsider the use of the left ideals of the even-grade subalgebra of spacetime algebra to describe fermionic excitations. When interpreted as rotors the general elements of an even-grade left-ideal describe massless particles in chiral flavour doublets. To study the application of these ideas to the standard Dirac formalism I construct a $2 \\times 2$-matrix representation with bivector insertions for the Dirac algebra. This algebra has four ideals, and this approach clarifies how the identification of Dirac $\\g_{\\mu}$-matrices with orthonormal basisvectors ${\\bf e}_{\\nu}$ annihilates half of the ideals. For one possible choice of this mapping the remaining ideals the chiral left- and righthanded components of the fermion coincide with the even- and odd elements of spacetime algebra.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-07-17T19:44:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94B27",
      "17B81",
      "15A66"
    ],
    "keywords": [
      "dirac fermions",
      "spacetime algebra",
      "standard dirac formalism",
      "chiral flavour doublets",
      "orthonormal basisvectors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 735841,
      "adsabs": "2006math.ph..12081W"
    }
  }
}