{
  "id": "hep-th/0101092",
  "version": "v1",
  "published": "2001-01-15T08:11:53.000Z",
  "updated": "2001-01-15T08:11:53.000Z",
  "title": "Pythagoras' Theorem on a 2D-Lattice from a \"Natural\" Dirac Operator and Connes' Distance Formula",
  "authors": [
    "Jian Dai",
    "Xing-Chang Song"
  ],
  "comment": "Latex 11pages, no figures",
  "journal": "J.Phys.A34:5571-5582,2001",
  "doi": "10.1088/0305-4470/34/27/307",
  "categories": [
    "hep-th",
    "hep-lat",
    "math-ph",
    "math.MP"
  ],
  "abstract": "One of the key ingredients of A. Connes' noncommutative geometry is a generalized Dirac operator which induces a metric(Connes' distance) on the state space. We generalize such a Dirac operator devised by A. Dimakis et al, whose Connes' distance recovers the linear distance on a 1D lattice, into 2D lattice. This Dirac operator being \"naturally\" defined has the so-called \"local eigenvalue property\" and induces Euclidean distance on this 2D lattice. This kind of Dirac operator can be generalized into any higher dimensional lattices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-01-15T08:11:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirac operator",
      "distance formula",
      "pythagoras",
      "2d-lattice",
      "2d lattice"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 539899
    }
  }
}