What question did this study set out to answer?

This research aims to extend a pole reduction algorithm to derive differential operators associated with Feynman integrals.

April 17, 2026Open Access

Picard-Fuchs Equations of Twisted Differential forms associated to Feynman Integrals

Key Points

This research aims to extend a pole reduction algorithm to derive differential operators associated with Feynman integrals.
Applied the Griffiths-Dwork pole reduction algorithm.
Derived D-modules of differential operators.
Examined twisted Picard-Fuchs operators for specific differential motives.
Presented new twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives.
Illustrated the effective computation of twisted period integrals from Feynman integrals.

Abstract

Dimensionally or analytically regulated Feynman integrals lead to relative twisted period integrals. We present a recent extension of the Griffiths-Dwork pole reduction algorithm for deriving the D-module of differential operators acting on the twisted differential forms from Feynman integrals. We illustrate the application of this algorithm by providing twisted Picard-Fuchs operators for hypergeometric, elliptic and Calabi-Yau differential motives arising from families of Feynman integrals.

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Discussion

Authors

Pierre Vanhove

Actions

References and Citations

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Picard-Fuchs Equations of Twisted Differential forms associated to Feynman Integrals

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Actions

References and Citations

Citation Network

Connected Papers

Discussion

Cite this study