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Publisher’s description: This volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews. The book aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.
The articles of this volume will be reviewed individually.
Indexed articles:
Blümlein, Johannes, Analytic integration methods in quantum field theory: an introduction, 1-33 [Zbl 1484.81104]
Ablinger, Jakob, Extensions of the AZ-algorithm and the package multiintegrate, 35-61 [Zbl 1490.33010]
Acres, Kevin; Broadhurst, David, Empirical determinations of Feynman integrals using integer relation algorithms, 63-82 [Zbl 1484.81077]
Bartels, Jochen, \(N = 4\) SYM gauge theories: the \(2 \rightarrow 6\) amplitude in the Regge limit, 83-106 [Zbl 1484.81038]
Bourjaily, Jacob L.; He, Yang-Hui; McLeod, Andrew J.; Spradlin, Marcus; Vergu, Cristian; Volk, Matthias; von Hippel, Matt; Wilhelm, Matthias, Direct integration for multi-leg amplitudes: tips, tricks, and when they fail, 107-123 [Zbl 1484.81039]
Broedel, Johannes; Kaderli, André, A geometrical framework for amplitude recursions: bridging between trees and loops, 125-144 [Zbl 1484.81093]
Dreyfus, Thomas; Weil, Jacques-Arthur, Differential Galois theory and integration, 145-171 [Zbl 1489.12019]
Frellesvig, Hjalte, Top-down decomposition: a cut-based approach to integral reductions, 173-188 [Zbl 1484.81040]
Kalmykov, Mikhail; Bytev, Vladimir; Kniehl, Bernd A.; Moch, Sven-Olaf; Ward, Bennie F. L.; Yost, Scott A., Hypergeometric functions and Feynman diagrams, 189-234 [Zbl 1489.33010]
Kotikov, Anatoly V., Differential equations and Feynman integrals, 235-259 [Zbl 1484.81041]
Koutschan, Christoph, Holonomic anti-differentiation and Feynman amplitudes, 261-277 [Zbl 1484.81042]
Kreimer, Dirk, Outer space as a combinatorial backbone for Cutkosky rules and coactions, 279-312 [Zbl 1484.81043]
Marquard, Peter, Integration-by-parts: a survey, 313-320 [Zbl 1484.81044]
Moch, Sven-Olaf; Magerya, Vitaly, Calculating four-loop corrections in QCD, 321-334 [Zbl 1484.81099]
Paule, Peter, Contiguous relations and creative telescoping, 335-394 [Zbl 1482.33016]
Raab, Clemens G., Nested integrals and rationalizing transformations, 395-422 [Zbl 1487.68257]
Schneider, Carsten, Term algebras, canonical representations and difference ring theory for symbolic summation, 423-485 [Zbl 1484.81078]
Smirnov, Vladimir A., Expansion by regions: an overview, 487-499 [Zbl 1503.81032]
Vermaseren, J. A. M., Some steps towards improving IBP calculations and related topics, 501-518 [Zbl 1478.81004]
Weinzierl, Stefan, Iterated integrals related to Feynman integrals associated to elliptic curves, 519-545 [Zbl 1478.81015]