{
  "id": "1209.2021",
  "version": "v1",
  "published": "2012-09-10T15:06:59.000Z",
  "updated": "2012-09-10T15:06:59.000Z",
  "title": "Dirac operator on spinors and diffeomorphisms",
  "authors": [
    "Ludwik Dabrowski",
    "Giacomo Dossena"
  ],
  "comment": "13 pages",
  "journal": "Class. Quantum Grav. 30 015006 (2013)",
  "doi": "10.1088/0264-9381/30/1/015006",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\\sigma$ and Riemannian metric $g$ there is associated a space $S_{\\sigma, g}$ of spinor fields on $M$ and a Hilbert space $\\HH_{\\sigma, g}= L^2(S_{\\sigma, g},\\vol{M}{g})$ of $L^2$-spinors of $S_{\\sigma, g}$. The group $\\diff{M}$ of orientation-preserving diffeomorphisms of $M$ acts both on $g$ (by pullback) and on $[\\sigma]$ (by a suitably defined pullback $f^*\\sigma$). Any $f\\in \\diff{M}$ lifts in exactly two ways to a unitary operator $U$ from $\\HH_{\\sigma, g} $ to $\\HH_{f^*\\sigma,f^*g}$. The canonically defined Dirac operator is shown to be equivariant with respect to the action of $U$, so in particular its spectrum is invariant under the diffeomorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-10T15:06:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C27",
      "15A66",
      "34L40",
      "57S05"
    ],
    "keywords": [
      "diffeomorphisms",
      "riemannian metric",
      "spin structure",
      "spinor fields",
      "general covariance"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP",
      "journal": "Classical and Quantum Gravity",
      "year": 2013,
      "month": "Jan",
      "volume": 30,
      "number": 1,
      "pages": "015006"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1185172,
      "adsabs": "2013CQGra..30a5006D"
    }
  }
}