{
  "id": "1301.3480",
  "version": "v1",
  "published": "2013-01-15T20:36:44.000Z",
  "updated": "2013-01-15T20:36:44.000Z",
  "title": "Gauge networks in noncommutative geometry",
  "authors": [
    "Matilde Marcolli",
    "Walter D. van Suijlekom"
  ],
  "comment": "30 pages",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. The configuration space of quiver representations (modulo equivalence) in the category of finite spectral triples is studied; gauge networks appear as an orthonormal basis in a corresponding Hilbert space. We give many examples of gauge networks, also beyond the well-known spin network examples. We find a Hamiltonian operator on this Hilbert space, inducing a time evolution on the C*-algebra of gauge network correspondences. Given a representation in the category of spectral triples of a quiver embedded in a spin manifold, we define a discretized Dirac operator on the quiver. We compute the spectral action of this Dirac operator on a four-dimensional lattice, and find that it reduces to the Wilson action for lattice gauge theories and a Higgs field lattice system. As such, in the continuum limit it reduces to the Yang-Mills-Higgs system. For the three-dimensional case, we relate the spectral action functional to the Kogut-Susskind Hamiltonian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-15T20:36:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "noncommutative geometry",
      "lattice gauge",
      "dirac operator",
      "hilbert space",
      "well-known spin network examples"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.geomphys.2013.09.002",
      "journal": "Journal of Geometry and Physics",
      "year": 2014,
      "month": "Jan",
      "volume": 75,
      "pages": 71
    },
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1210913,
      "adsabs": "2014JGP....75...71M"
    }
  }
}