Combinatorial Dyson–Schwinger equations in noncommutative field theory

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 $B_{+}^{\gamma }$ 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.