{
  "id": "hep-th/0002181",
  "version": "v9",
  "published": "2000-02-22T10:47:48.000Z",
  "updated": "2000-10-10T16:59:47.000Z",
  "title": "Fractal index, central charge and fractons",
  "authors": [
    "Wellington da Cruz",
    "Rosevaldo de Oliveira"
  ],
  "comment": "latex, 12 pages, To appear in Mod. Phys. Lett. A (2000)",
  "journal": "Mod.Phys.Lett. A15 (2000) 1931-1940",
  "doi": "10.1142/S0217732300002206",
  "categories": [
    "hep-th",
    "cond-mat"
  ],
  "abstract": "We introduce the notion of fractal index associated with the universal class $h$ of particles or quasiparticles, termed fractons, which obey specific fractal statistics. A connection between fractons and conformal field theory(CFT)-quasiparticles is established taking into account the central charge $c[\\nu]$ and the particle-hole duality $\\nu\\longleftrightarrow\\frac{1}{\\nu}$, for integer-value $\\nu$ of the statistical parameter. In this way, we derive the Fermi velocity in terms of the central charge as $v\\sim\\frac{c[\\nu]}{\\nu+1}$. The Hausdorff dimension $h$ which labelled the universal classes of particles and the conformal anomaly are therefore related. Following another route, we also established a connection between Rogers dilogarithm function, Farey series of rational numbers and the Hausdorff dimension.",
  "revisions": [
    {
      "version": "v9",
      "updated": "2000-10-10T16:59:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central charge",
      "fractal index",
      "hausdorff dimension",
      "obey specific fractal statistics",
      "conformal field theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 524198
    }
  }
}