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Computer Algebra in Quantum Field Theory

Integration, Summation and Special Functions

  • Book
  • © 2013

Overview

Editors:
  1. Carsten Schneider

    1. RISC, Johannes Kepler University, Linz, Austria

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    You can also search for this editor in PubMed   Google Scholar

  2. Johannes Blümlein

    1. DESY, Zeuthen, Germany

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    You can also search for this editor in PubMed   Google Scholar

  • 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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Harmonic Sums, Polylogarithms,Special Numbers, and Their Generalizations

    • Jakob Ablinger, Johannes Blümlein
    Pages 1-32

  3. Multiple Zeta Values and Modular Forms in Quantum Field Theory

    • David Broadhurst
    Pages 33-73

  4. Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order

    • Stefan Gerhold, Manuel Kauers, Christoph Koutschan, Peter Paule, Carsten Schneider, Burkhard Zimmermann
    Pages 75-96

  5. Conformal Methods for Massless Feynman Integrals and Large N f Methods

    • John A. Gracey
    Pages 97-118

  6. The Holonomic Toolkit

    • Manuel Kauers
    Pages 119-144

  7. Orthogonal Polynomials

    • Tom H. Koornwinder
    Pages 145-170

  8. Creative Telescoping for Holonomic Functions

    • Christoph Koutschan
    Pages 171-194

  9. Renormalization and Mellin Transforms

    • Dirk Kreimer, Erik Panzer
    Pages 195-223

  10. Relativistic Coulomb Integrals and Zeilberger’s Holonomic Systems Approach. I

    • Peter Paule, Sergei K. Suslov
    Pages 225-241

  11. Hypergeometric Functions in Mathematica ®

    • Oleksandr Pavlyk
    Pages 243-258

  12. Solving Linear Recurrence Equations with Polynomial Coefficients

    • Marko Petkovšek, Helena Zakrajšek
    Pages 259-284

  13. Generalization of Risch’s Algorithm to Special Functions

    • Clemens G. Raab
    Pages 285-304

  14. Multiple Hypergeometric Series: Appell Series and Beyond

    • Michael J. Schlosser
    Pages 305-324

  15. Simplifying Multiple Sums in Difference Fields

    • Carsten Schneider
    Pages 325-360

  16. Potential of FORM 4.0

    • Jos A. M. Vermaseren
    Pages 361-379

  17. Feynman Graphs

    • Stefan Weinzierl
    Pages 381-406

  18. Back Matter

    Pages 407-411
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Keywords

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.

Reviews

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)

Editors and Affiliations

  • RISC, Johannes Kepler University, Linz, Austria

    Carsten Schneider

  • DESY, Zeuthen, Germany

    Johannes Blümlein

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