{
  "id": "hep-th/9411201",
  "version": "v2",
  "published": "1994-11-28T13:30:58.000Z",
  "updated": "1994-11-29T08:04:45.000Z",
  "title": "Thirring Model as a Gauge Theory",
  "authors": [
    "Taichi Itoh",
    "Yoonbai Kim",
    "Masaki Sugiura",
    "Koichi Yamawaki"
  ],
  "comment": "33 pages",
  "journal": "Prog.Theor.Phys. 93 (1995) 417-440",
  "doi": "10.1143/PTP.93.417",
  "categories": [
    "hep-th",
    "hep-lat",
    "hep-ph"
  ],
  "abstract": "We reformulate the Thirring model in $D$ $(2 \\le D < 4)$ dimensions as a gauge theory by introducing $U(1)$ hidden local symmetry (HLS) and study the dynamical mass generation of the fermion through the Schwinger-Dyson (SD) equation. By virtue of such a gauge symmetry we can greatly simplify the analysis of the SD equation by taking the most appropriate gauge (``nonlocal gauge'') for the HLS. In the case of even-number of (2-component) fermions, we find the dynamical fermion mass generation as the second order phase transition at certain fermion number, which breaks the chiral symmetry but preserves the parity in (2+1) dimensions ($D=3$). In the infinite four-fermion coupling (massless gauge boson) limit in (2+1) dimensions, the result coincides with that of the (2+1)-dimensional QED, with the critical number of the 4-component fermion being $N_{\\rm cr} = \\frac{128}{3\\pi^{2}}$. As to the case of odd-number (2-component) fermion in (2+1) dimensions, the regularization ambiguity on the induced Chern-Simons term may be resolved by specifying the regularization so as to preserve the HLS. Our method also applies to the (1+1) dimensions, the result being consistent with the exact solution. The bosonization mechanism in (1+1) dimensional Thirring model is also reproduced in the context of dual-transformed theory for the HLS.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1994-11-29T08:04:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gauge theory",
      "dimensions",
      "second order phase transition",
      "dynamical fermion mass generation",
      "hidden local symmetry"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 380349
    }
  }
}