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.
