{
  "id": "1602.00468",
  "version": "v1",
  "published": "2016-02-01T10:48:27.000Z",
  "updated": "2016-02-01T10:48:27.000Z",
  "title": "Hamiltonian constraint formulation of classical field theories",
  "authors": [
    "Vaclav Zatloukal"
  ],
  "comment": "21 pages. arXiv admin note: substantial text overlap with arXiv:1504.08344",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined via the (Hamiltonian) constraint between multivector-valued generalized momenta, and points in the configuration space. Starting from a variational principle, we derive the local equations of motion, that is, differential equations that determine classical surfaces and momenta. A local Hamilton-Jacobi equation applicable in the field theory then follows readily. In addition, we discuss the relation between symmetries and conservation laws, and derive a Hamiltonian version of the Noether theorem, where the Noether currents are identified as the classical momentum contracted with the symmetry-generating vector fields. The general formalism is illustrated by two examples: the scalar field theory, and the string theory. Throughout the article, we employ the mathematical formalism of geometric algebra and calculus, which allows us to perform completely coordinate-free manipulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-01T10:48:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical field theory",
      "hamiltonian constraint formulation",
      "configuration space",
      "scalar field theory",
      "local hamilton-jacobi equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160200468Z",
      "inspire": 1418888
    }
  }
}