Feynman integrals and motives

Details Feynman integrals and motives Feynman integrals and motives

2009-07-02

arxiv.org/abs/0907.0321v1

Physics

Mathematical Physics

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

Scientific paper

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.

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