The geometry of one-loop amplitudes
High Energy Physics - Theory
2010-10-27 v1
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.
Cite
@article{arxiv.1010.5334,
title = {The geometry of one-loop amplitudes},
author = {Oliver Schnetz},
journal= {arXiv preprint arXiv:1010.5334},
year = {2010}
}
Comments
23 pages, 8 figures