TY  - GEN
AU  - Weinzierl,Stefan
TI  - Feynman Integrals : A Comprehensive Treatment for Students and Researchers 
T2  - Unitext for physics
SN  - 9783030995577 (HB)
PY  - 2022///
CY  - Switzerland
PB  - Springer
KW  - Feynman integrals
KW  - Feynman-Graph
N1  - 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
N2  - 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
ER  -