JournalsjncgVol. 7, No. 1pp. 255–289

Combinatorial Dyson–Schwinger equations in noncommutative field theory

  • Adrian Tanasă

    École Polytechnique, Palaiseau, France
  • Dirk Kreimer

    Boston University, USA
Combinatorial Dyson–Schwinger equations in noncommutative field theory cover
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Abstract

We introduce here the Hopf algebra structure describing the noncommutative renormalization of a recently introduced translation-invariant model on Moyal space. We define Hochschild one-cocyles B+γB_+^\gamma which allows us to write down the combinatorial Dyson–Schwinger equations for noncommutative quantum field theory. One- and two-loops examples are explicitly worked out.

Cite this article

Adrian Tanasă, Dirk Kreimer, Combinatorial Dyson–Schwinger equations in noncommutative field theory. J. Noncommut. Geom. 7 (2013), no. 1, pp. 255–289

DOI 10.4171/JNCG/116