Feynman integrals and motives

Abstract

This article gives an overview of recent results on the relation between quantum field theory and motives, with an emphasis on two different approaches: a "bottom-up" approach based on the algebraic geometry of varieties associated to Feynman graphs, and a "top-down" approach based on the comparison of the properties of associated categorical structures. This survey is mostly based on joint work of the author with Paolo Aluffi, along the lines of the first approach, and on previous work of the author with Alain Connes on the second approach.

32 pages LaTeX, 3 figures, to appear in the Proceedings of the 5th European Congress of Mathematics

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Cited by in corpus (7)

• Prescriptive Unitarity
• Framings for graph hypersurfaces
• Position Space Equations for Banana Feynman Diagrams
• New realizations of modular forms in Calabi-Yau threefolds arising from ${\varphi }^4$ theory
• Regularized Integrals on Riemann Surfaces and Modular Forms
• Co-homology of Differential Forms and Feynman diagrams
• Feynman quadrics-motive of the massive sunset graph