FEYNMAN MOTIVES

The book explores the intricate relationship between Feynman integrals in quantum field theory and the theory of motives in algebraic geometry. It addresses the pivotal question of when the residues of these integrals correspond to periods of mixed Tate motives, stemming from earlier observations of multiple zeta values. Two distinct methodologies are examined: a "bottom-up" approach that constructs algebraic varieties from Feynman graphs, and a "top-down" approach that compares renormalization data with Tannakian categories of mixed Tate motives. The text also highlights ongoing research and connections to various mathematical fields.