Feynman Integrals
A Comprehensive Treatment for Students and Researchers
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Beschreibung
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.
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
Autor*in
Stefan Weinzierl
Themen in »Feynman Integrals«
Perturbation Theory Multiple Polylogarithms Cluster Algebras Graph Polynomials Iterated Integrals GKZ Systems Hopf Algebras
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“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)
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