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  • © 2021

Anti-Differentiation and the Calculation of Feynman Amplitudes

  • Presents 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

Part of the book series: Texts & Monographs in Symbolic Computation (TEXTSMONOGR)

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eBook USD 129.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-80219-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 169.99
Price excludes VAT (USA)
Hardcover Book USD 169.99
Price excludes VAT (USA)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xiii
  2. Direct Integration for Multi-Leg Amplitudes: Tips, Tricks, and When They Fail

    • Jacob L. Bourjaily, Yang-Hui He, Andrew J. McLeod, Marcus Spradlin, Cristian Vergu, Matthias Volk et al.
    Pages 107-123
  3. Differential Galois Theory and Integration

    • Thomas Dreyfus, Jacques-Arthur Weil
    Pages 145-171
  4. Hypergeometric Functions and Feynman Diagrams

    • Mikhail Kalmykov, Vladimir Bytev, Bernd A. Kniehl, Sven-Olaf Moch, Bennie F. L. Ward, Scott A. Yost
    Pages 189-234
  5. Differential Equations and Feynman Integrals

    • Anatoly V. Kotikov
    Pages 235-259
  6. Holonomic Anti-Differentiation and Feynman Amplitudes

    • Christoph Koutschan
    Pages 261-277
  7. Integration-by-Parts: A Survey

    • Peter Marquard
    Pages 313-320
  8. Calculating Four-Loop Corrections in QCD

    • Sven-Olaf Moch, Vitaly Magerya
    Pages 321-334
  9. Expansion by Regions: An Overview

    • Vladimir A. Smirnov
    Pages 487-499

About this book

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.


Keywords

  • elliptic integrals and functions
  • iterated modular functions
  • iterated integrals
  • massive high loop Feynman integral
  • differential equations

Editors and Affiliations

  • Deutsches Elektronen-Synchrotron, DESY, Zeuthen, Germany

    Johannes Blümlein

  • Research Institute for Symbolic Computation, Johannes Kepler University Linz, Linz, Austria

    Carsten Schneider

Bibliographic Information

Buying options

eBook USD 129.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-80219-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 169.99
Price excludes VAT (USA)
Hardcover Book USD 169.99
Price excludes VAT (USA)