{
  "id": "math-ph/0501037",
  "version": "v1",
  "published": "2005-01-12T17:00:46.000Z",
  "updated": "2005-01-12T17:00:46.000Z",
  "title": "The number of eigenvalues for an Hamiltonian in Fock space",
  "authors": [
    "Sergio Albeverio",
    "Saidakhmat N. Lakaev",
    "Tulkin H. Rasulov"
  ],
  "comment": "23 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "A model operator $H$ corresponding to the energy operator of a system with non-conserved number $n\\leq 3$ of particles is considered. The precise location and structure of the essential spectrum of $H$ is described. The existence of infinitely many eigenvalues below the bottom of the essential spectrum of $H$ is proved if the generalized Friedrichs model has a virtual level at the bottom of the essential spectrum and for the number $N(z)$ of eigenvalues below $z<0$ an asymptotics established. The finiteness of eigenvalues of $H$ below the bottom of the essential spectrum is proved if the generalized Friedrichs model has a zero eigenvalue at the bottom of its essential spectrum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-12T17:00:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "35P20",
      "47N50"
    ],
    "keywords": [
      "essential spectrum",
      "fock space",
      "generalized friedrichs model",
      "hamiltonian",
      "model operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.ph...1037A"
    }
  }
}