{
  "id": "1011.0524",
  "version": "v1",
  "published": "2010-11-02T06:53:56.000Z",
  "updated": "2010-11-02T06:53:56.000Z",
  "title": "From Quantum Mechanics to Quantum Field Theory: The Hopf route",
  "authors": [
    "Allan I. Solomon",
    "Gérard Henry Edmond Duchamp",
    "Pawel Blasiak",
    "Andrzej Horzela",
    "Karol A. Penson"
  ],
  "journal": "J.Phys.Conf.Ser.284:012055,2011",
  "doi": "10.1088/1742-6596/284/1/012055",
  "categories": [
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "We show that the combinatorial numbers known as {\\em Bell numbers} are generic in quantum physics. This is because they arise in the procedure known as {\\em Normal ordering} of bosons, a procedure which is involved in the evaluation of quantum functions such as the canonical partition function of quantum statistical physics, {\\it inter alia}. In fact, we shall show that an evaluation of the non-interacting partition function for a single boson system is identical to integrating the {\\em exponential generating function} of the Bell numbers, which is a device for encapsulating a combinatorial sequence in a single function. We then introduce a remarkable equality, the Dobinski relation, and use it to indicate why renormalisation is necessary in even the simplest of perturbation expansions for a partition function. Finally we introduce a global algebraic description of this simple model, giving a Hopf algebra, which provides a starting point for extensions to more complex physical systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-02T06:53:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum field theory",
      "quantum mechanics",
      "hopf route",
      "partition function",
      "bell numbers"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics Conference Series",
      "year": 2011,
      "month": "Mar",
      "volume": 284,
      "number": 1,
      "pages": "012055"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 875498,
      "adsabs": "2011JPhCS.284a2055S"
    }
  }
}