Feynman Integrals

This textbook on Feynman integrals starts from the basics, requiring only knowledge of special relativity and undergraduate mathematics. Feynman integrals are indispensable for precision calculations in quantum field theory. At the same time, they are also fascinating from a mathematical point of view. Topics from quantum field theory and advanced mathematics are introduced as needed.
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.

Covers the exciting development in the field of Feynman integrals of the last 15 years Offers a pedagogical style: Students at the beginning of their master degree should be able to follow the book Includes many exercises with solutions

Autorentext

Stefan Weinzierl is Professor for theoretical high energy physics at Johannes Gutenberg Universität Mainz, Germany. His research interests include precision calculations in particle physics, multiple polylogarithms and elliptic generalizations, gravity and gauge theories as well as jet physics and top quark physics.

Inhalt
Introduction.- Basics.- Graph polynomials.- Quantum eld 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.