Read more
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.
List of contents
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.
About the author
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.
Report
"This book provides a detailed and up-to-date introduction to Feynman integrals ... . The book is written in a very didactic way. ... the book gives an excellent introduction to the field of Feynman integrals at the level of a master's/starting Ph.D. student ... . The structure of the book and the fact that it contains many exercises make it a very useful resource for a course on this topic." (Samuel Abreu, Mathematical Reviews, December, 2023)
