JournalsjncgVol. 7 , No. 1DOI 10.4171/jncg/116

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

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.