{
  "id": "quant-ph/0002041",
  "version": "v1",
  "published": "2000-02-15T00:10:08.000Z",
  "updated": "2000-02-15T00:10:08.000Z",
  "title": "Symplectic areas, quantization, and dynamics in electromagnetic fields",
  "authors": [
    "M. V. Karasev",
    "T. A. Osborn"
  ],
  "comment": "39 pages, 17 figures",
  "journal": "J. Math. Phys. 43:756-788, 2002",
  "doi": "10.1063/1.1426688",
  "categories": [
    "quant-ph"
  ],
  "abstract": "A gauge invariant quantization in a closed integral form is developed over a linear phase space endowed with an inhomogeneous Faraday electromagnetic tensor. An analog of the Groenewold product formula (corresponding to Weyl ordering) is obtained via a membrane magnetic area, and extended to the product of N symbols. The problem of ordering in quantization is related to different configurations of membranes: a choice of configuration determines a phase factor that fixes the ordering and controls a symplectic groupoid structure on the secondary phase space. A gauge invariant solution of the quantum evolution problem for a charged particle in an electromagnetic field is represented in an exact continual form and in the semiclassical approximation via the area of dynamical membranes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-02-15T00:10:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "electromagnetic field",
      "symplectic areas",
      "quantum evolution problem",
      "gauge invariant solution",
      "secondary phase space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}