Periods of Feynman Diagrams and GKZ D-Modules
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.
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