{
  "id": "math-ph/0202001",
  "version": "v3",
  "published": "2002-02-01T16:57:48.000Z",
  "updated": "2003-02-20T08:31:13.000Z",
  "title": "One non-relativistic particle coupled to a photon field",
  "authors": [
    "Christian Hainzl"
  ],
  "comment": "final version, to appear in Ann. Henri Poincare",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate the ground state energy of an electron coupled to a photon field. First, we regard the self-energy of a free electron, which we describe by the Pauli-Fierz Hamiltonian. We show that, in the case of small values of the coupling constant $\\alpha$, the leading order term is represented by $2\\pi^{-1} \\alpha (\\Lambda - \\ln[1 + \\Lambda])$. Next we put the electron in the field of an arbitrary external potential $V$, such that the corresponding Schr\\\"odinger operator $p^2 + V$ has at least one eigenvalue, and show that by coupling to the radiation field the binding energy increases, at least for small enough values of the coupling constant $\\alpha$. Moreover, we provide concrete numbers for $\\alpha$, the ultraviolet cut-off $\\Lambda$, and the radiative correction for which our procedure works.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-02-20T08:31:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81V10"
    ],
    "keywords": [
      "photon field",
      "non-relativistic particle",
      "ground state energy",
      "arbitrary external potential",
      "coupling constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.ph...2001H"
    }
  }
}