Feynman integrals a comprehensive treatment for students and researchers / [electronic resource] :

• 作者： Weinzierl, Stefan.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • UNITEXT for physics.
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： UNITEXT for physics,
• 主題： Feynman integrals. , Elementary Particles, Quantum Field Theory. , Mathematical Physics. , Quantum Physics. , Theoretical, Mathematical and Computational Physics. , Algebraic Geometry.
• ISBN： 9783030995584 (electronic bk.) 、 9783030995577 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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.
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• 摘要註: 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.
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