{
  "id": "1605.09736",
  "version": "v1",
  "published": "2016-05-31T17:31:29.000Z",
  "updated": "2016-05-31T17:31:29.000Z",
  "title": "Trigonometric and elliptic Ruijsenaars-Schneider systems on the complex projective space",
  "authors": [
    "L. Feher",
    "T. F. Gorbe"
  ],
  "comment": "18 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present a direct construction of compact real forms of the trigonometric and elliptic $n$-particle Ruijsenaars-Schneider systems whose completed center-of-mass phase space is the complex projective space $\\mathbb{CP}^{n-1}$ with the Fubini-Study symplectic structure. These systems are labelled by an integer $p\\in\\{1,\\dots,n-1\\}$ relative prime to $n$ and a coupling parameter $y$ varying in a certain punctured interval around $p\\pi/n$. Our work extends Ruijsenaars's pioneering study of compactifications that imposed the restriction $0<y<\\pi/n$, and also builds on an earlier derivation of more general compact trigonometric systems by Hamiltonian reduction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-31T17:31:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex projective space",
      "elliptic ruijsenaars-schneider systems",
      "work extends ruijsenaarss pioneering study",
      "general compact trigonometric systems",
      "completed center-of-mass phase space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}