Feynman diagrams as a completely integrable lattice statistical system

Abstract

We consider the application of the Yang-Baxter equation in multiloop calculations in quantum field theory. An important (from the point of view of the physical applications) problem in the analytical evaluations of massless multi-loop Feynman integrals is the representation of the D-dimensional integral. The analytical evaluations of the multi-loop Feynman integrals are usually
based on such powerful methods as the integration by parts and star-triangle (uniqueness) relation methods.
In this paper we investigated Feynman diagrams with massless scalar propagators are shown to be equivalent to some completely integrable lattice system. In this work we take the large order dimensional ( D = 8, D = 12 ) diagram and have proved some equations, obtained partition function of lattice. So we gеt some results which describe a lattice statistical system, using these methods for large order dimensional.