%0 Journal Article
%T A geometrical angle on Feynman integrals
%A A. I. Davydychev
%A R. Delbourgo
%J Mathematics
%D 1997
%I arXiv
%R 10.1063/1.532513
%X A direct link between a one-loop N-point Feynman diagram and a geometrical representation based on the N-dimensional simplex is established by relating the Feynman parametric representations to the integrals over contents of (N-1)-dimensional simplices in non-Euclidean geometry of constant curvature. In particular, the four-point function in four dimensions is proportional to the volume of a three-dimensional spherical (or hyperbolic) tetrahedron which can be calculated by splitting into birectangular ones. It is also shown that the known formula of reduction of the N-point function in (N-1) dimensions corresponds to splitting the related N-dimensional simplex into N rectangular ones.
%U http://arxiv.org/abs/hep-th/9709216v2