{
  "id": "0808.3819",
  "version": "v1",
  "published": "2008-08-28T16:04:36.000Z",
  "updated": "2008-08-28T16:04:36.000Z",
  "title": "Towards a definition of quantum integrability",
  "authors": [
    "J. Clemente-Gallardo",
    "G. Marmo"
  ],
  "comment": "37 pages, AmsLatex, 1 figure",
  "journal": "Int.J.Geom.Meth.Mod.Phys.6:129-172,2009",
  "doi": "10.1142/S0219887809003448",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to the quantum framework would not work because all infinite dimensional Hilbert spaces are unitarily isomorphic and, as a consequence, it would not be easy to define degrees of freedom. We argue that a geometrical formulation of quantum mechanics might provide a way out.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-28T16:04:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "02.40.Yy",
      "03.65.Ca",
      "02.30.Ik"
    ],
    "keywords": [
      "quantum integrability",
      "definition",
      "infinite dimensional hilbert spaces",
      "relevant aspects",
      "complete integrability"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "International Journal of Geometric Methods in Modern Physics",
      "year": 2009,
      "number": 1,
      "pages": 129
    },
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 794196,
      "adsabs": "2009IJGMM..06..129C"
    }
  }
}