{
  "id": "1411.7673",
  "version": "v1",
  "published": "2014-11-27T18:32:10.000Z",
  "updated": "2014-11-27T18:32:10.000Z",
  "title": "On the chirality of a discrete Dirac-Kähler equation",
  "authors": [
    "Volodymyr Sushch"
  ],
  "comment": "18 pages. arXiv admin note: substantial text overlap with arXiv:1307.1220",
  "categories": [
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "We discuss a discrete analogue of the Dirac-K\\\"{a}hler equation in which chiral properties of the continual counterpart are captured. We pay special attention to a discrete Hodge star operator. To build one a combinatorial construction of double complex is used. We describe discrete exterior calculus operations on a double comlex and obtain the discrete Dirac-K\\\"{a}hler equation using these tools. Self-dual and anti-self-dual discrete inhomogeneous forms are presented. The chiral invariance of the massless discrete Dirac-K\\\"{a}hler equation is shown. Moreover, in the massive case we prove that a discrete Dirac-K\\\"{a}hler operator flips the chirality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-27T18:32:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39A12",
      "39A70",
      "35Q41"
    ],
    "keywords": [
      "discrete dirac-kähler equation",
      "discrete exterior calculus operations",
      "discrete hodge star operator",
      "pay special attention",
      "anti-self-dual discrete inhomogeneous forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1332559,
      "adsabs": "2014arXiv1411.7673S"
    }
  }
}