{
  "id": "2008.07765",
  "version": "v1",
  "published": "2020-08-18T06:55:16.000Z",
  "updated": "2020-08-18T06:55:16.000Z",
  "title": "Explicit Computations for the Classical and Quantum Integrability of the 3-Dimensional Rational Calogero-Moser System",
  "authors": [
    "Yana Staneva"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The integrability of the classical and quantum rational Calogero-Moser systems is verified explicitly via the Lax pair method for the case $n=3$. We provide an extensive survey of reflection groups and root systems. The Olshanetsky-Perelomov operators are constructed for a general root system via Dunkl operators, associated to root systems. The integrability of the quantum rational Calogero-Moser system is discussed via the Olshanetsky-Perelomov operators, which provide a set of commuting integrals of motion. The classical analogues of both the Dunkl and the Olshanetsky-Perelomov operators are also presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-18T06:55:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70H06",
      "37J35"
    ],
    "keywords": [
      "quantum integrability",
      "explicit computations",
      "quantum rational calogero-moser system",
      "olshanetsky-perelomov operators",
      "general root system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}