Position space approach to equations for Feynman integrals

Abstract: Studying Feynman loop integrals attracts a lot of attention nowadays, with a plethora of methods being developed. Among those, a rather effective is the differential equation method. It serves both as a computational tool and a potential classification principle. It appears that the equations involved are somewhat simpler than the special functions to which the loop integrals evaluate. I will describe a new approach to deriving these equations based on the position space properties of propagators. We will see how equations obtained from the Calabi-Yau geometry of banana/sunset graphs can be obtained directly from the Klein-Gordon equation.