Combinatorial Dyson–Schwinger equations in noncommutative field theory

• DOI: 10.4171/jncg/116
• Publication Date: 2013-03-08T08:58:39Z
• Authors: Adrian Tanasă; Dirk Kreimer
• Keywords: High Energy Physics - Theory; High Energy Physics - Theory (hep-th); 0103 physical sciences; FOS: Physical sciences; Mathematical Physics (math-ph); 01 natural sciences; Mathematical Physics

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