{
  "id": "hep-th/0311243",
  "version": "v1",
  "published": "2003-11-25T14:54:07.000Z",
  "updated": "2003-11-25T14:54:07.000Z",
  "title": "Kontsevich product and gauge invariance",
  "authors": [
    "Ashok Das",
    "Josif Frenkel"
  ],
  "comment": "7 pages",
  "journal": "Phys.Rev.D69:065017,2004",
  "doi": "10.1103/PhysRevD.69.065017",
  "categories": [
    "hep-th"
  ],
  "abstract": "We analyze the question of $U_{\\star} (1)$ gauge invariance in a flat non-commutative space where the parameter of non-commutativity, $\\theta^{\\mu\\nu} (x)$, is a local function satisfying Jacobi identity (and thereby leading to an associative Kontsevich product). We show that in this case, both gauge transformations as well as the definitions of covariant derivatives have to modify so as to have a gauge invariant action. We work out the gauge invariant actions for the matter fields in the fundamental and the adjoint representations up to order $\\theta^{2}$ while we discuss the gauge invariant Maxwell theory up to order $\\theta$. We show that despite the modifications in the gauge transformations, the covariant derivative and the field strength, Seiberg-Witten map continues to hold for this theory. In this theory, translations do not form a subgroup of the gauge transformations (unlike in the case when $\\theta^{\\mu\\nu}$ is a constant) which is reflected in the stress tensor not being conserved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-25T14:54:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11.15.-q",
      "11.10.Nx"
    ],
    "keywords": [
      "gauge invariance",
      "kontsevich product",
      "gauge transformations",
      "gauge invariant action",
      "gauge invariant maxwell theory"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. D"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 634008
    }
  }
}