{
  "id": "1308.2455",
  "version": "v3",
  "published": "2013-08-12T03:49:42.000Z",
  "updated": "2014-05-02T05:59:43.000Z",
  "title": "Relativistic helicity and link in Minkowski space-time",
  "authors": [
    "Z. Yoshida",
    "Y. Kawazura",
    "T. Yokoyama"
  ],
  "journal": "J. Math. Phys. 55 (2014), 043101 1--19",
  "doi": "10.1063/1.4872236",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A relativistic helicity has been formulated in the four-dimensional Minkowski space-time. Whereas the relativistic distortion of space-time violates the conservation of the conventional helicity, the newly defined relativistic helicity conserves in a barotropic fluid or plasma, dictating a fundamental topological constraint. The relation between the helicity and the vortex-line topology has been delineated by analyzing the linking number of vortex filaments which are singular differential forms representing the pure states of Banach algebra. While the dimension of space-time is four, vortex filaments link, because vorticities are primarily 2-forms and the corresponding 2-chains link in four dimension; the relativistic helicity measures the linking number of vortex filaments that are proper-time cross-sections of the vorticity 2-chains. A thermodynamic force yields an additional term in the vorticity, by which the vortex filaments on a reference-time plane are no longer pure states. However, the vortex filaments on a proper-time plane remain to be pure states, if the thermodynamic force is exact (barotropic), thus, the linking number of vortex filaments conserves.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-02T05:59:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pure states",
      "linking number",
      "thermodynamic force yields",
      "newly defined relativistic helicity conserves",
      "vortex filaments link"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 2014,
      "month": "Apr",
      "volume": 55,
      "number": 4,
      "pages": "043101"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JMP....55d3101Y"
    }
  }
}