A geometrical angle on Feynman integrals
摘要
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.
引用
@article{arxiv.hep-th/9709216,
title = {A geometrical angle on Feynman integrals},
author = {A. I. Davydychev and R. Delbourgo},
journal= {arXiv preprint arXiv:hep-th/9709216},
year = {2008}
}
备注
47 pages, including 42 pages of the text (in plain Latex) and 5 pages with the figures (in a separate Latex file, requires axodraw.sty) a note and three references added, minor problem with notation fixed