Titlebook: Anti-Differentiation and the Calculation of Feynman Amplitudes; Johannes Blümlein,Carsten Schneider Book 2021 The Editor(s) (if applicable

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Book 2021rmany, 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 sp

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Book 2021of 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..

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A Geometrical Framework for Amplitude Recursions: Bridging Between Trees and Loops,variable of a differential equation of KZ or KZB type. The parameter interpolates between two associated regularized boundary values, which contain iterated integrals closely related to scattering amplitudes defined on two different geometries.

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Top-Down Decomposition: A Cut-Based Approach to Integral Reductions,pproach. This approach can be seen as an integral level version of the algorithms based on integrand reduction and generalized unitarity cuts, that were revolutionizing NLO scattering computations in the early 2000s.

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Mathematisch-physikalische Bibliothekvariable of a differential equation of KZ or KZB type. The parameter interpolates between two associated regularized boundary values, which contain iterated integrals closely related to scattering amplitudes defined on two different geometries.

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Exkurs: Algebraische Strukturen,agram in dimension .?=?3???2. is not expressible in terms of multiple polylogarithms. Another interesting example is the Puiseux-type solution involving a differential operator generated by a hypergeometric function of three variables. The holonomic properties of the .. hypergeometric functions are briefly discussed.

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https://doi.org/10.1007/978-3-322-83837-7such graphs simple graphs. The Dunce’s cap graph is the first non-simple graph. The number of its spanning trees (five) exceeds the number of its edges (four). We compare the two coactions which indeed do not agree and discuss this result. We also point out that for kinematic renormalization schemes the coaction .. simplifies.