Johannes Blümlein

Carsten Schneider

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.

Anti-Differentiation and the Calculation of Feynman Amplitudes

The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.

Integration, Summation and Special Functions

Computer Algebra in Quantum Field Theory

Tord Riemann

Proceedings of the 5th Zeuthen Workshop on Elementary Particle Theory, Loops and Legs in Quantum Field Theory, Bastei, Germany, 9-14 April, 2000

Loops and Legs in Quantum Field Theory

Loops and Legs in Quantum Field Theory : Proceedings of the 6th International Symposium on Radiative Corrections and the 6th Zeuthen Workshop on Elementary Particle Theory

Application of Quantum Field Theory to Phenomenology -- RADCOR 2002

Jürgen Brunner

New Exclusion Limits for Dark Gauge Forces from Beam-dump Data

New Exclusion Limits on Dark Gauge Forces from Proton Bremsstrahlung in Beam-dump Data

Peter Paule

This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.

Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory

Johannes Blümlein

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