{
  "id": "1410.3249",
  "version": "v1",
  "published": "2014-10-13T10:15:02.000Z",
  "updated": "2014-10-13T10:15:02.000Z",
  "title": "Lagrange-Dirac systems for charged particles in gauge fields",
  "authors": [
    "Fernando Jimenez"
  ],
  "comment": "Comments are welcome! arXiv admin note: text overlap with arXiv:1405.0748 by other authors",
  "categories": [
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "In this work, we use the Sternberg phase space (which may be considered as the classical phase space of particles in gauge fields) in order to explore the dynamics of such particles in the context of Lagrange-Dirac systems and their associated Hamilton-Pontryagin variational principles. For this, we develop an analogue of the Pontryagin bundle in the case of the Sternberg phase space. Moreover, we show the link of this new bundle to the so-called magnetized Tulczyjew triple, which is an analogue of the link between the Pontryagin bundle and the usual Tulczyjew triple. Taking advantage of the symplectic nature of the Sternberg space, we induce a Dirac structure on the Sternberg-Pontryagin bundle which leads to the Lagrange-Dirac structure that we are looking for. We also analyze the intrinsic and variational nature of the equations of motion of particles in gauge fields in regards of the defined new geometry. Lastly, we illustrate our theory through the case of a $U(1)$ gauge group, leading to the paradigmatic example of a electricaly charged particle in an electromagnetic field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-13T10:15:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gauge fields",
      "lagrange-dirac systems",
      "charged particle",
      "sternberg phase space",
      "pontryagin bundle"
    ],
    "publication": {
      "doi": "10.1016/j.geomphys.2015.03.011",
      "journal": "Journal of Geometry and Physics",
      "year": 2015,
      "month": "Aug",
      "volume": 94,
      "pages": 35
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JGP....94...35J"
    }
  }
}