In quantum field theory, the Connes-Kreimer Hopf algebra captures not only the structure of perturbative renormalization but allows also to describe the non-perturbative regime in terms of “combinatorial” Dyson-Schwinger equations. This algebra generalizes from usual Feyn- man diagrams to “strand graphs”, the combinatorial objects underlying a broad class of non-local theories, in particular tensorial field theory. Here we show how this can be used to derive Dyson-Schwinger equa- tions in the case of φ^4 theory with tensorial interactions.
Keywords: Quantum Field Theory; Renormalization; Dyson-Schwinger Equations