{
  "id": "0910.5158",
  "version": "v2",
  "published": "2009-10-27T16:19:16.000Z",
  "updated": "2010-07-08T10:41:01.000Z",
  "title": "Noncommutative geometry, gauge theory and renormalization",
  "authors": [
    "Axel de Goursac"
  ],
  "comment": "159 pages, 14 figures, PhD thesis, v2: revised version",
  "journal": "Verlag Dr Muller (2010)",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "math.OA",
    "math.QA",
    "math.RA"
  ],
  "abstract": "Nowadays, noncommutative geometry is a growing domain of mathematics, which can appear as a promising framework for modern physics. Quantum field theories on \"noncommutative spaces\" are indeed much investigated, and suffer from a new type of divergence called the ultraviolet-infrared mixing. However, this problem has recently been solved by H. Grosse and R. Wulkenhaar by adding to the action of a noncommutative scalar model a harmonic term, which renders it renormalizable. One aim of this thesis is the extension of this procedure to gauge theories on the Moyal space. Indeed, we have introduced a new noncommutative gauge theory, strongly related to the Grosse-Wulkenhaar model, and candidate to renormalizability. We have then studied the most important properties of this action, and in particular its vacuum configurations. Finally, we give a mathematical interpretation of this new action in terms of a derivation-based differential calculus associated to a superalgebra. This work contains among the results of this PhD, an introduction to noncommutative geometry, an introduction to epsilon-graded algebras, and an introduction to renormalization of scalar (wilsonian and BPHZ point of view) and gauge quantum field theories.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-07-08T10:41:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "noncommutative geometry",
      "renormalization",
      "gauge quantum field theories",
      "introduction",
      "noncommutative scalar model"
    ],
    "tags": [
      "dissertation",
      "journal article"
    ],
    "publication": {
      "journal": "Ph.D. Thesis",
      "year": 2009,
      "month": "Oct"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 159,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 835811,
      "adsabs": "2009PhDT.......198D"
    }
  }
}