{
  "id": "math-ph/0406061",
  "version": "v2",
  "published": "2004-06-24T16:43:09.000Z",
  "updated": "2005-11-04T14:37:42.000Z",
  "title": "Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model",
  "authors": [
    "Edwin Langmann"
  ],
  "comment": "21 pages, v2: title changed, otherwise only minor corrections",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We present further remarkable functional identities related to the elliptic Calogero-Sutherland (eCS) system. We derive them from a second quantization of the eCS model within a quantum field theory model of anyons on a circle and at finite temperature. The identities involve two eCS Hamiltonians with arbitrary and, in general, different particle numbers $N$ and $M$, and a particular function of $N+M$ variables arising as anyon correlation function of $N$ particles and $M$ anti-particles. In addition to identities obtained from anyons with the same statistics parameter $\\lambda$, we also obtain ``dual'' relations involving ``mixed'' correlation functions of anyons with two different statistics parameters $\\lambda$ and $1/\\lambda$. We also give alternative, elementary proofs of these identities by direct computations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-11-04T14:37:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q58",
      "81T40"
    ],
    "keywords": [
      "elliptic calogero-sutherland model",
      "identities",
      "statistics parameter",
      "quantum field theory model",
      "anyon correlation function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 653113,
      "adsabs": "2004math.ph...6061L"
    }
  }
}