Periods of Feynman Diagrams and GKZ D-Modules

Understand

We study differential equations for Feynman amplitudes and we 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 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.