The geometry of one-loop amplitudes
arXiv:1010.5334
Abstract
We review a reduction formula by Petersson that reduces the calculation of a one-loop amplitude with N external lines in n<N space-time dimensions to the case n=N and give it a geometric interpretation. In the case n=N the calculation of the euclidean amplitude is shown to be equivalent to the calculation of the volume of a tetrahedron spanned by the momenta in (n-1)-dimensional hyperbolic space. The underlying geometry is intimately linked to the geometry of the reduction formula.
23 pages, 8 figures