{
  "id": "1306.5597",
  "version": "v1",
  "published": "2013-06-24T12:33:19.000Z",
  "updated": "2013-06-24T12:33:19.000Z",
  "title": "Isospectral deformations of the Dirac operator",
  "authors": [
    "Oliver Knill"
  ],
  "comment": "32 pages, 8 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We give more details about an integrable system in which the Dirac operator D=d+d^* on a finite simple graph G or Riemannian manifold M is deformed using a Hamiltonian system D'=[B,h(D)] with B=d-d^* + i b. The deformed operator D(t) = d(t) + b(t) + d(t)^* defines a new exterior derivative d(t) and a new Dirac operator C(t) = d(t) + d(t)^* and Laplacian M(t) = d(t) d(t)^* + d(t)* d(t) and so a new distance on G or a new metric on M.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-24T12:33:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37K15",
      "81R12",
      "57M15",
      "81Q60"
    ],
    "keywords": [
      "dirac operator",
      "isospectral deformations",
      "finite simple graph",
      "riemannian manifold",
      "hamiltonian system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.5597K"
    }
  }
}