{
  "id": "1310.0318",
  "version": "v3",
  "published": "2013-10-01T14:24:34.000Z",
  "updated": "2015-01-27T11:37:41.000Z",
  "title": "A Characterization of Invariant Connections",
  "authors": [
    "Maximilian Hanusch"
  ],
  "journal": "SIGMA 10 (2014), 025, 25 pages",
  "doi": "10.3842/SIGMA.2014.025",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Given a principal fibre bundle with structure group $S$, and a fibre transitive Lie group $G$ of automorphisms thereon, Wang's theorem identifies the invariant connections with certain linear maps $\\psi\\colon \\mathfrak{g}\\rightarrow \\mathfrak{s}$. In the present paper, we prove an extension of this theorem which applies to the general situation where $G$ acts non-transitively on the base manifold. We consider several special cases of the general theorem, including the result of Harnad, Shnider and Vinet which applies to the situation where $G$ admits only one orbit type. Along the way, we give applications to loop quantum gravity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-15T06:28:48.000Z",
      "abstract": "Given a principal fibre bundle with structure group $S$ and a fibre transitive Lie group $G$ of automorphisms thereon, Wang's theorem identifies the invariant connections with certain linear maps $\\psi\\colon \\mathfrak{g}\\rightarrow \\mathfrak{s}$. In the present paper we prove an extension of this theorem that applies to the general situation where $G$ acts non-transitively on the base manifold. We consider several special cases of the general theorem including the result of Harnad, Shnider and Vinet which applies to the situation where $G$ admits only one orbit type. Along the way we give applications to loop quantum gravity.",
      "comment": null,
      "journal": "SIGMA 10 (2014), 025, 24 pages"
    },
    {
      "version": "v3",
      "updated": "2015-01-27T11:37:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22F50",
      "53C05"
    ],
    "keywords": [
      "invariant connections",
      "characterization",
      "principal fibre bundle",
      "wangs theorem identifies",
      "loop quantum gravity"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2014,
      "month": "Mar",
      "volume": 10,
      "pages": "025"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1294994,
      "adsabs": "2014SIGMA..10..025H"
    }
  }
}