Periods of Feynman Diagrams

Author: Nasrollahpoursamami, Emad

Year: 2017

Degree: Dissertation (Ph.D.)

Advisor: Marcolli, Matilde

Committee Members: Marcolli, Matilde; Rains, Eric M.; Zhu, Xinwen; Graber, Thomas B.

Option: Mathematics

DOI: 10.7907/Z9GX48MR

Abstract

We study differential equations for Feynman amplitudes and show that the corresponding D-module is isomorphic to a GKZ D-modules. We show that the sheaf of solutions to the D-module is isomorphic to a certain relative homology and that the amplitudes are periods of a relative motive. Using these ideas, we develop a method of regularization which specializes to dimensional regularization and analytic regularization.

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