{
  "id": "math-ph/0004020",
  "version": "v3",
  "published": "2000-04-17T18:14:10.000Z",
  "updated": "2000-04-24T19:56:05.000Z",
  "title": "Hamiltonian formalism with several variables and quantum field theory, PartI",
  "authors": [
    "Frederic Helein",
    "Joseph Kouneiher"
  ],
  "comment": "minor modifications in the introduction and ref. added. (42 pages)",
  "categories": [
    "math-ph",
    "gr-qc",
    "hep-th",
    "math.DS",
    "math.MP"
  ],
  "abstract": "We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\\it{pataplectic}} hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the Poisson $\\mathfrak{p}$-brackets and $\\mathfrak{\\omega}$-brackets which are the analogues of the Poisson bracket on forms. We formulate the equations of motion of forms in terms of $\\mathfrak{p}$-brackets and $\\mathfrak{\\omega}$-brackets with the $n$-form ${\\cal H}\\omega $. As illustration of our formalism we present two examples: the interacting scalar fields and conformal string theory.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2000-04-24T19:56:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum field theory",
      "hamiltonian formalism",
      "classical field theory",
      "legendre correspondance",
      "poisson bracket"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 526282,
      "adsabs": "2000math.ph...4020H"
    }
  }
}