{
  "id": "1310.5750",
  "version": "v2",
  "published": "2013-10-21T22:47:20.000Z",
  "updated": "2016-06-29T18:12:55.000Z",
  "title": "Hamiltonian analysis for linearly acceleration-dependent Lagrangians",
  "authors": [
    "Miguel Cruz",
    "Rosario Gomez-Cortes",
    "Alberto Molgado",
    "Efrain Rojas"
  ],
  "comment": "33 pages, no figures",
  "journal": "J. Math. Phys. 57 062903 (2016)",
  "doi": "10.1063/1.4954804",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defned quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies together with a Noether charge may be identifed. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for the Hamiltonian formulation of covariant feld theories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-21T22:47:20.000Z",
      "title": "Hamiltonian dynamics of linear affine in acceleration theories",
      "abstract": "We study the constrained Ostrogradski-Hamilton framework for the equations of motion $M_{\\mu \\nu} \\ddot{x}^\\nu = F_\\mu (x^\\nu,\\dot{x}^\\nu)$ provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories, and its relation to the inherent conserved quantities, where the associated energies together with a N\\\"oether charge may be identified. We also provide some examples where our approach is explicitly applied, and emphasize the way in which our original arrangement results propitious for the Hamiltonian formulation of covariant field theories.",
      "comment": "24 pages, no figures",
      "journal": null,
      "doi": null,
      "authors": [
        "Miguel Cruz",
        "Alberto Molgado",
        "Efrain Rojas"
      ]
    },
    {
      "version": "v2",
      "updated": "2016-06-29T18:12:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70H45",
      "70H50"
    ],
    "keywords": [
      "hamiltonian dynamics",
      "linear affine",
      "acceleration theories",
      "covariant field theories",
      "constrained ostrogradski-hamilton framework"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1261803,
      "adsabs": "2013arXiv1310.5750C"
    }
  }
}