© 2012

Analytic Tools for Feynman Integrals

  • Most powerful methods of evaluating Feynman integrals are presented

  • Reader will be able to apply them in practice

  • Contains numerous examples


Part of the Springer Tracts in Modern Physics book series (STMP, volume 250)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Vladimir A. Smirnov
    Pages 1-10
  3. Vladimir A. Smirnov
    Pages 11-31
  4. Vladimir A. Smirnov
    Pages 33-59
  5. Vladimir A. Smirnov
    Pages 61-81
  6. Vladimir A. Smirnov
    Pages 83-126
  7. Vladimir A. Smirnov
    Pages 127-155
  8. Vladimir A. Smirnov
    Pages 157-172
  9. Vladimir A. Smirnov
    Pages 203-226
  10. Vladimir A. Smirnov
    Pages 227-236
  11. Vladimir A. Smirnov
    Pages 237-241
  12. Vladimir A. Smirnov
    Pages 243-257
  13. Vladimir A. Smirnov
    Pages 259-273
  14. Vladimir A. Smirnov
    Pages 275-292
  15. Back Matter
    Pages 293-296

About this book


The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice.  This book supersedes the author’s previous Springer book “Evaluating Feynman Integrals” and its textbook version “Feynman Integral Calculus.” Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often public.

In comparison to the two previous books, three new chapters have been added:  One is on sector decomposition, while the second describes a new method by Lee. The third new chapter concerns the asymptotic expansions of Feynman integrals in momenta and masses, which were described in detail in another Springer book, “Applied Asymptotic Expansions in Momenta and Masses,” by the author. This chapter describes, on the basis of papers that appeared after the publication of said book, how to algorithmically discover the regions relevant to a given limit within the strategy of expansion by regions. In addition, the chapters on the method of Mellin-Barnes representation and on the method of integration by parts have been substantially rewritten, with an emphasis on the corresponding algorithms and computer codes.


Alpha and Feynman parameters Dimensional regularization Evaluating Feynman integrals Feynman integrals Master Baikov's Method Mellin-Barnes representation Solve Reduction Problems Solving Feynman integrals

Authors and affiliations

  1. 1.Skobeltsyn Institute of Nuclear Physics, Div. of Theoretical High-Energy PhysicsMoscow State UniversityMoscowRussia

About the authors

Dr. V. A. Smirnov
Moscow State University

Bibliographic information