{
  "id": "math-ph/0011043",
  "version": "v1",
  "published": "2000-11-27T13:15:30.000Z",
  "updated": "2000-11-27T13:15:30.000Z",
  "title": "The infrared behaviour in Nelson's model of a quantum particle coupled to a massless scalar field",
  "authors": [
    "Jozsef Lorinczi",
    "Robert A. Minlos",
    "Herbert Spohn"
  ],
  "journal": "Annales Henri Poincare 3 (2002) 269-295",
  "categories": [
    "math-ph",
    "math.GT",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We prove that Nelson's massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian and the Hamiltonian obtained from Euclidean quantization are not unitarily equivalent. In contrast, for dimensions higher than three the Nelson Hamiltonian has a unique ground state in Fock space and the two Hamiltonians are unitarily equivalent. We also show that the Euclidean Hamiltonian has no spectral gap.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-11-27T13:15:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum particle",
      "nelsons model",
      "infrared behaviour",
      "nelson hamiltonian",
      "nelsons massless scalar field model"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00023-002-8617-6"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 537550,
      "adsabs": "2000math.ph..11043L"
    }
  }
}