A GEOMETRICAL ANGLE ON FEYNMAN-INTEGRALS

A direct link between a one-loop N-point Feynman diagram and a geometr ical representation based on the N-dimensional simplex is established by relating the Feynman parametric representations to the integrals ov er 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 spher ical (or hyperbolic);tetrahedron;which can be calculated by splitting into birectangular ones. It is also shown that the known formula of re duction of the N-point function in (N- I) dimensions corresponds to sp litting the related N-dimensional simplex into N rectangular ones. (C) 1998 American Institute of Physics.