Twisted Cohomology and Feynman Integrals

Abstract

This thesis has two aims. The primary aim is to introduce the intersection product method of evaluating families of Feynman integrals, and to put it into physical and mathematical context. In order to achieve this, we consider Feynman integrals and IBP relations between such integrals. We then define and consider a local system and the twisted cohomology of said system, proving multiply properties of either. This includes the existence of a Morse function which can be used to calculate the cohomology. We then define the intersection product on the twisted cohomology and consider its properties. The secondary aim is to judge how well the method does in practice. We compute a few examples and argue that the method is suitable for Feynman diagrams with a low number of loops, while being less suitable for higher loop counts.