Halting problem in Feynman graphon processes derived from the renormalization Hopf algebra

Abstract

Thanks to the theory of graphons and random graphs, Feynman graphons are new analytic tools for the study of infinities in (strongly coupled) gauge field theories. We formulate the Halting problem in Feynman graphon processes to build a new theory of computation in dealing with solutions of combinatorial Dyson–Schwinger equations in the context of the Turing machines and Manin’s renormalization Hopf algebra.