Subsystems via quantum motions

Thanks to the topological Hopf algebra of renormalization of Green’s functions in a gauge field theory, we associate a bi-Heyting algebra to each combinatorial Dyson–Schwinger equation. This setting leads us to characterize subsystems generated by the solution spaces of quantum motions. In addition, we apply the \(c_{2}\) $c_2$ -invariant of Feynman diagrams to build a new Heyting algebra of multiplicative groups which encodes a more general class of subsystems of the physical theory.