Singularities and MZVs in Feynman Loop Integrals (Various aspects of multiple zeta values)

Abstract

Feynman diagram is a theoretical tool for computing physical quantities in particle physics, and each diagram is given as a multiple integral. Often Feynman diagrams can be expressed by multiple zeta values (MZVs) and their generalizations. We discuss relations between singularities of diagrams and types of MZVs from a physicist's viewpoint. This provides a hint to a connection between topology of a diagram and its value in terms of MZVs. New technologies for computing complicated diagrams and unsolved problems are also discussed.