{
  "id": "hep-th/9912253",
  "version": "v1",
  "published": "1999-12-27T07:24:32.000Z",
  "updated": "1999-12-27T07:24:32.000Z",
  "title": "Note on the Gauge Fixing in Gauge Theory",
  "authors": [
    "Kazuo Fujikawa",
    "Hiroaki Terashima"
  ],
  "comment": "12 pages",
  "journal": "Nucl.Phys. B577 (2000) 405-415",
  "doi": "10.1016/S0550-3213(00)00102-4",
  "categories": [
    "hep-th",
    "hep-lat",
    "hep-ph"
  ],
  "abstract": "In the absence of Gribov complications, the modified gauge fixing in gauge theory $ \\int{\\cal D}A_{\\mu}\\{\\exp[-S_{YM}(A_{\\mu})-\\int f(A_{\\mu})dx] /\\int{\\cal D}g\\exp[-\\int f(A_{\\mu}^{g})dx]\\}$ for example, $f(A_{\\mu})=(1/2)(A_{\\mu})^{2}$, is identical to the conventional Faddeev-Popov formula $\\int{\\cal D}A_{\\mu}\\{\\delta(D^{\\mu}\\frac{\\delta f(A_{\\nu})}{\\delta A_{\\mu}})/\\int {\\cal D}g\\delta(D^{\\mu}\\frac{\\delta f(A_{\\nu}^{g})} {\\delta A_{\\mu}^{g}})\\}\\exp[-S_{YM}(A_{\\mu})]$ if one takes into account the variation of the gauge field along the entire gauge orbit. Despite of its quite different appearance,the modified formula defines a local and BRST invariant theory and thus ensures unitarity at least in perturbation theory. In the presence of Gribov complications, as is expected in non-perturbative Yang-Mills theory, the modified formula is equivalent to the conventional formula but not identical to it:Both of the definitions give rise to non-local theory in general and thus the unitarity is not obvious. Implications of the present analysis on the lattice regularization are briefly discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-12-27T07:24:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gauge theory",
      "gauge fixing",
      "gribov complications",
      "entire gauge orbit",
      "brst invariant theory"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Nucl. Phys. B"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 512514
    }
  }
}