{
  "id": "0911.5126",
  "version": "v1",
  "published": "2009-11-26T17:19:45.000Z",
  "updated": "2009-11-26T17:19:45.000Z",
  "title": "On the spectral analysis of many-body systems",
  "authors": [
    "Mondher Damak",
    "Vladimir Georgescu"
  ],
  "comment": "This is a strongly modified version of arXiv:0806.0827v1 so we preferred to change the title",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We describe the essential spectrum and prove the Mourre estimate for quantum particle systems interacting through k-body forces and creation-annihilation processes which do not preserve the number of particles. For this we compute the ``Hamiltonian algebra'' of the system, i.e. the C*-algebra C generated by the Hamiltonians we want to study, and show that, as in the N-body case, it is graded by a semilattice. Hilbert C*-modules graded by semilattices are involved in the construction of C. For example, if we start with an N-body system whose Hamiltonian algebra is B and then we add field type couplings between subsystems, then the many-body Hamiltonian algebra C is the imprimitivity algebra of a graded Hilbert B-module.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-26T17:19:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "46L60",
      "47L90"
    ],
    "keywords": [
      "spectral analysis",
      "many-body systems",
      "add field type couplings",
      "quantum particle systems",
      "many-body hamiltonian algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.5126D"
    }
  }
}