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

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Einführung in die Kinderheilkundeen limit where some kinematic invariants and/or masses have certain scaling measured in powers of a given small parameter. Prescriptions of this strategy are formulated in a simple geometrical language and are illustrated through simple examples.

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Johannes Blümlein,Carsten SchneiderPresents up-to-date reviews on modular forms and functions and their use in particle physics.Combines knowledge from mathematical physics and mathematics.Written by international authors

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Texts & Monographs in Symbolic Computationhttp://image.papertrans.cn/a/image/158329.jpg

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Exkurs: Algebraische Strukturen,The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion coefficients are shown, and modern methods based on differential equations are discussed.

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https://doi.org/10.1007/978-3-322-83837-7Computer algebra methods within the scope of the holonomic systems approach provide a versatile toolbox to integration problems in the context of Feynman diagrams. This is demonstrated with the aid of several benchmark problems, ranging from hypergeometric series evaluations to Bessel integrals of sunrise diagrams.

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Einführung in die KinderheilkundeA number of aspects of IBP reductions are discussed, indicating some of the major bottlenecks. Potential future developments are indicated, including some in the realm of mathematics and computer algebra.

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Differential Equations and Feynman Integrals,The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion coefficients are shown, and modern methods based on differential equations are discussed.

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Holonomic Anti-Differentiation and Feynman Amplitudes,Computer algebra methods within the scope of the holonomic systems approach provide a versatile toolbox to integration problems in the context of Feynman diagrams. This is demonstrated with the aid of several benchmark problems, ranging from hypergeometric series evaluations to Bessel integrals of sunrise diagrams.