A geometrical angle on Feynman integrals

Details A geometrical angle on Feynman integrals A geometrical angle on Feynman integrals

1997-09-30

arxiv.org/abs/hep-th/9709216v2

J.Math.Phys.39:4299-4334,1998

Physics

High Energy Physics

High Energy Physics - Theory

47 pages, including 42 pages of the text (in plain Latex) and 5 pages with the figures (in a separate Latex file, requires axo

Scientific paper

10.1063/1.532513

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.

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