Position Space Feynman quadrics and their motives

Abstract

In this note, we introduce and study position space Feynman quadrics that are the loci of divergences of the position space Feynman integrals for Euclidean massless scalar quantum field theories. We prove that the Feynman quadrics define objects in the category of mixed Tate motives for complete graphs with a bound on the number of vertices. This result shows a strong contrast with the graph hypersurfaces approach which produces also non-mixed Tate examples.