{
  "id": "math-ph/0403061",
  "version": "v1",
  "published": "2004-03-30T14:15:37.000Z",
  "updated": "2004-03-30T14:15:37.000Z",
  "title": "Gauge fields and Sternberg-Weinstein Approximation of Poisson Manifolds",
  "authors": [
    "Oliver Maspfuhl"
  ],
  "comment": "48 pages, no figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The motion of a classical particle in a gravitational and a Yang-Mills field was described by S. Sternberg and A. Weinstein by a particular Hamiltonian system on a Poisson manifold known under the name of Sternberg-Weinstein phase space. This system leads to the generalization of the Lorentz equation of motion first discovered by Wong. The aim of this work is to show that inversely, a Hamiltonian H on a general Poisson manifold, with the property that its differential vanishes on a Lagrangian submanifold X of a symplectic leaf and is generic in any other direction, naturally defines a metric on X, as well as a principal connection form on a canonical principal fiber bundle on X. These fields, which are credited to model a gravitational and a Yang-Mills field on X, respectively, define a linearized Hamiltonian system of Wong type on a canonical linearized Poisson manifold at X locally isomorphic to a Sternberg-Weinstein phase space. In addition, H is shown to define scalar fields which first appeared in a theory of Einstein and Mayer. In the presence of a coisotropic constraint, the reduced system can be regarded as the phase space of particles in gravitational, Yang-Mills and Higgs fields. We further show that all our constructions are locally related to usual gauge and Kaluza-Klein theory via symplectic realization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-03-30T14:15:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D17"
    ],
    "keywords": [
      "gauge fields",
      "sternberg-weinstein approximation",
      "sternberg-weinstein phase space",
      "yang-mills field",
      "hamiltonian system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 647303,
      "adsabs": "2004math.ph...3061M"
    }
  }
}