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arxiv: 1302.0670 · v2 · submitted 2013-02-04 · ✦ hep-th · hep-ph· math.AG

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Periods and Hodge structures in perturbative quantum field theory

Stefan Weinzierl
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classification ✦ hep-th hep-phmath.AG
keywords fieldhodgeperiodsperturbativequantumsidestructurestheory
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There is a fruitful interplay between algebraic geometry on the one side and perturbative quantum field theory on the other side. I review the main relevant mathematical concepts of periods, Hodge structures and Picard-Fuchs equations and discuss the connection with Feynman integrals.

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

    math.AG 2026-04 unverdicted novelty 6.0

    An extension of the Griffiths-Dwork algorithm produces twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives from families of Feynman integrals.