{
  "id": "1207.2814",
  "version": "v4",
  "published": "2012-07-12T00:25:06.000Z",
  "updated": "2013-06-18T11:04:00.000Z",
  "title": "The Hamilton-Pontryagin Principle and Multi-Dirac Structures for Classical Field Theories",
  "authors": [
    "Joris Vankerschaver",
    "Hiroaki Yoshimura",
    "Melvin Leok"
  ],
  "comment": "Uses RevTeX; this article supersedes arXiv:1008.0252",
  "journal": "J. Math. Phys. 53, nr. 7 (2012)",
  "doi": "10.1063/1.4731481",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce a variational principle for field theories, referred to as the Hamilton-Pontryagin principle, and we show that the resulting field equations are the Euler-Lagrange equations in implicit form. Secondly, we introduce multi-Dirac structures as a graded analog of standard Dirac structures, and we show that the graph of a multisymplectic form determines a multi-Dirac structure. We then discuss the role of multi-Dirac structures in field theory by showing that the implicit Euler-Lagrange equations for fields obtained from the Hamilton-Pontryagin principle can be described intrinsically using multi-Dirac structures. Lastly, we show a number of illustrative examples, including time-dependent mechanics, nonlinear scalar fields, Maxwell's equations, and elastostatics.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-06-18T11:04:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "field theory",
      "multi-dirac structure",
      "hamilton-pontryagin principle",
      "classical field theories",
      "implicit euler-lagrange equations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 2012,
      "month": "Jul",
      "volume": 53,
      "number": 7,
      "pages": "072903"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JMP....53g2903V"
    }
  }
}