Systems of Linear Dyson–Schwinger Equations

Systems of Dyson–Schwinger equation represent the equations of motion in quantum field theory. In this paper, we follow the combinatorial approach and consider Dyson–Schwinger equations as fixed point equations that determine the perturbation series by usage of graph insertion operators. We discuss their properties under the renormalization flow, prove that fixed points are scheme independent, and construct solutions for coupled systems with linearized arguments of the insertion operators.