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arxiv: 0810.1313 · v1 · submitted 2008-10-07 · 🧮 math.AG

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Motives associated to sums of graphs

Spencer Bloch
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classification 🧮 math.AG
keywords graphsassociatedmotivemotivessubringaffineamplitudebelkale
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The Feynman amplitude associated to a graph is a period of a certain motive. The sum of these motive classes over all connected graphs with no multiple edges or tadpoles and n vertices is defined in the Grothendieck ring of varieties. This sum is shown to lie in the subring generated by the affine line. It follows from work of Belkale and Brosnan that motives of individual graphs do not lie in this subring.

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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.