Feynman integrals: a comprehensive treatment for students and researchers/ Stefan Weinzierl

Includes bibliography and index

Introduction -- Basics -- Graph polynomials -- Quantum field theory -- One-loop integrals -- Iterated integrals -- Transformations of differential equations -- Multiple polylogarithms -- Nested sums -- Sector decomposition -- Hopf algebras coactions and symbols -- Cluster algebras -- Elliptic curves -- Motives and mixed Hodge structures -- Numerics -- Final project

The book covers modern developments in the field of Feynman integrals. Topics included are: representations of Feynman integrals, integration-by-parts, differential equations, intersection theory, multiple polylogarithms, Gelfand-Kapranov-Zelevinsky systems, coactions and symbols, cluster algebras, elliptic Feynman integrals, and motives associated with Feynman integrals. This volume is aimed at a) students at the master's level in physics or mathematics, b) physicists who want to learn how to calculate Feynman integrals (for whom state-of-the-art techniques and computations are provided), and c) mathematicians who are interested in the mathematical aspects underlying Feynman integrals. It is, indeed, the interwoven nature of their physical and mathematical aspects that make Feynman integrals so enthralling.