{
  "id": "math-ph/0309044",
  "version": "v1",
  "published": "2003-09-18T05:22:07.000Z",
  "updated": "2003-09-18T05:22:07.000Z",
  "title": "Local exponents and infinitesimal generators of canonical transformations on Boson Fock spaces",
  "authors": [
    "F. Hiroshima",
    "K. R. Ito"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A one-parameter symplectic group $\\{e^{t\\dA}\\}_{t\\in\\RR}$ derives proper canonical transformations on a Boson Fock space. It has been known that the unitary operator $U_t$ implementing such a proper canonical transformation gives a projective unitary representation of $\\{e^{t\\dA}\\}_{t\\in\\RR}$ and that $U_t$ can be expressed as a normal-ordered form. We rigorously derive the self-adjoint operator $\\D(\\dA)$ and a phase factor $e^{i\\int_0^t\\TA(s)ds}$ with a real-valued function $\\TA$ such that $U_t=e^{i\\int_0^t\\TA(s)ds}e^{it\\D(\\dA)}$. Key words: Canonical transformations(Bogoliubov transformations), symplectic groups, projective unitary representations, one-parameter unitary groups, infinitesimal self-adjoint generators, local factors, local exponents, normal-ordered quadratic expressions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-09-18T05:22:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boson fock space",
      "local exponents",
      "infinitesimal generators",
      "projective unitary representation",
      "one-parameter symplectic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.ph...9044H"
    }
  }
}