© 2013

Computer Algebra in Quantum Field Theory

Integration, Summation and Special Functions

  • Carsten Schneider
  • Johannes Blümlein
  • Combines techniques methods from special functions and computer algebra applied to quantum field theory

  • Contains survey articles written by mathematicians and physicists

  • Describes algorithms and techniques developed by interdisciplinary teams of mathematicians, theoretical particle physicists and computer scientists


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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Jakob Ablinger, Johannes Blümlein
    Pages 1-32
  3. Stefan Gerhold, Manuel Kauers, Christoph Koutschan, Peter Paule, Carsten Schneider, Burkhard Zimmermann
    Pages 75-96
  4. Manuel Kauers
    Pages 119-144
  5. Tom H. Koornwinder
    Pages 145-170
  6. Christoph Koutschan
    Pages 171-194
  7. Dirk Kreimer, Erik Panzer
    Pages 195-223
  8. Oleksandr Pavlyk
    Pages 243-258
  9. Marko Petkovšek, Helena Zakrajšek
    Pages 259-284
  10. Carsten Schneider
    Pages 325-360
  11. Jos A. M. Vermaseren
    Pages 361-379
  12. Stefan Weinzierl
    Pages 381-406
  13. Back Matter
    Pages 407-411

About this book


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.


Difference and Differential Equations Feynman Integrals Special Functions Applied to QFT Symbolic Summation and Integration

Editors and affiliations

  • Carsten Schneider
    • 1
  • Johannes Blümlein
    • 2
  1. 1.RISC, Johannes Kepler UniversityLinzAustria
  2. 2.DESYZeuthenGermany

Bibliographic information


From the reviews:

“It is a collection of papers that grew out of a summer school course on integration, summation, and special functions in quantum field theory … . if you are interested in these sorts of special functions, and the computer algebra tools to manipulate them, whether or not your particular application is quantum field theory, then this book is an excellent description of the state of the art in computer algebra manipulation and proof.” (J. H. Davenport, Computing Reviews, April, 2014)