{
  "id": "1511.00828",
  "version": "v1",
  "published": "2015-11-03T09:25:57.000Z",
  "updated": "2015-11-03T09:25:57.000Z",
  "title": "Some reference formulas for the generating functions of canonical transformations",
  "authors": [
    "Damiano Anselmi"
  ],
  "comment": "25 pages, 8 figures",
  "categories": [
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then, we propose a standard way to express the generating function of a canonical transformation by means of a certain \"componential\" map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-03T09:25:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generating function",
      "canonical transformation",
      "reference formulas",
      "quantum field theory",
      "diagrammatic formula"
    ],
    "publication": {
      "doi": "10.1140/epjc/s10052-015-3874-y",
      "journal": "European Physical Journal C",
      "year": 2016,
      "month": "Feb",
      "volume": 76,
      "pages": 49
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016EPJC...76...49A",
      "inspire": 1402629
    }
  }
}