Feynman amplitudes on moduli spaces of graphs

Understand

This article introduces moduli spaces of coloured graphs on which Feynman amplitudes can be viewed as 'discrete' volume densities.

• The basic idea behind this construction is that these moduli spaces decompose into disjoint unions of open cells on which parametric Feynman integrals are defined in a natural way.
• Renormalisation of an amplitude translates then into the task of assigning to every cell a finite volume such that boundary relations between neighboring cells are respected.
• It is shown that this can be organized systematically using a type of Borel-Serre compactification of these moduli spaces.