{
  "id": "1407.7919",
  "version": "v2",
  "published": "2014-07-30T01:37:22.000Z",
  "updated": "2014-11-04T06:15:44.000Z",
  "title": "Particle Motion in Monopoles and Geodesics on Cones",
  "authors": [
    "Maxence Mayrand"
  ],
  "journal": "SIGMA 10 (2014), 102, 17 pages",
  "doi": "10.3842/SIGMA.2014.102",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The equations of motion of a charged particle in the field of Yang's $\\mathrm{SU}(2)$ monopole in 5-dimensional Euclidean space are derived by applying the Kaluza-Klein formalism to the principal bundle $\\mathbb{R}^8\\setminus\\{0\\}\\to\\mathbb{R}^5\\setminus\\{0\\}$ obtained by radially extending the Hopf fibration $S^7\\to S^4$, and solved by elementary methods. The main result is that for every particle trajectory $\\mathbf{r}:I\\to\\mathbb{R}^5\\setminus\\{0\\}$, there is a 4-dimensional cone with vertex at the origin on which $\\mathbf{r}$ is a geodesic. We give an explicit expression of the cone for any initial conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-30T01:37:22.000Z",
      "title": "Particle motion in monopoles and geodesics on cones",
      "comment": "18 pages, 2 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-04T06:15:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70H06",
      "34A26",
      "53B50"
    ],
    "keywords": [
      "particle motion",
      "main result",
      "euclidean space",
      "elementary methods",
      "kaluza-klein formalism"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2014,
      "month": "Nov",
      "volume": 10,
      "pages": 102
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1308980,
      "adsabs": "2014SIGMA..10..102M"
    }
  }
}