{
  "id": "math-ph/0103019",
  "version": "v3",
  "published": "2001-03-15T15:01:28.000Z",
  "updated": "2003-05-14T13:43:29.000Z",
  "title": "On the construction of K-operators in field theories as sections along Legendre maps",
  "authors": [
    "A. Echeverría-Enrí quez",
    "J. Marín-Solano",
    "M. C. Muñoz-Lecanda",
    "N. Román-Roy"
  ],
  "comment": "35 pages, LaTeX. Replaced with the edited version. The title has been changed. Minor details are corrected",
  "journal": "Acta Applicandae Mathematicae {\\bf 77}(1) (2003) 1-40",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The ``time-evolution operator'' in mechanics is a powerful tool which can be geometrically defined as a vector field along the Legendre map. It has been extensively used by several authors for studying the structure and properties of the dynamical systems (mainly the non-regular ones), such as the relation between the Lagrangian and Hamiltonian formalisms, constraints, and higher-order mechanics. This paper is devoted to defining a generalization of this operator for field theories, in a covariant formulation. In order to do this, we also use sections along maps, in particular multivector fields (skew-symmetric contravariant tensor fields of order greater than 1), jet fields and connection forms along the Legendre map. As a first relevant property, we use these geometrical objects to obtain the solutions of the Lagrangian and Hamiltonian field equations, and the equivalence among them (specially for non-regular field theories).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-05-14T13:43:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51P05",
      "43C05",
      "53C80",
      "55R10",
      "58A20",
      "58A30",
      "70S05"
    ],
    "keywords": [
      "legendre map",
      "construction",
      "skew-symmetric contravariant tensor fields",
      "k-operators",
      "non-regular field theories"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 554199,
      "adsabs": "2001math.ph...3019E"
    }
  }
}