标题： 费曼积分的几何角度 显示英文标题

标题： A geometrical angle on Feynman integrals

摘要： 建立了单圈N点费曼图与基于N维单纯形的几何表示之间的直接联系，通过将费曼参数表示关联到非欧几里得常曲率几何中(N-1)维单纯形的内容积分上。特别是，四维中的四点函数正比于三维球面（或双曲）四面体的体积，该体积可通过分割成双直角四面体来计算。还证明了已知的将N点函数约化为(N-1)维的公式对应于将相关的N维单纯形分割成N个矩形单纯形。 显示英文摘要

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.