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 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. 255–289DOI 10.4171/JNCG/116