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Feynman Integral Calculus

  • Textbook
  • © 2006

Overview

Authors:
  1. Vladimir A. Smirnov

    1. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia

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  • Problems and separate solutions

  • Comprehensive review of all tools to calculate and interprete Feynman Integrals

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-IX
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  2. Introduction

    • Vladimir A. Smirnov
    Pages 1-9

  3. Feynman Integrals: Basic Definitions and Tools

    • Vladimir A. Smirnov
    Pages 11-30

  4. Evaluating by Alpha and Feynman Parameters

    • Vladimir A. Smirnov
    Pages 31-55

  5. Evaluating by MB Representation

    • Vladimir A. Smirnov
    Pages 57-113

  6. IBP and Reduction to Master Integrals

    • Vladimir A. Smirnov
    Pages 115-138

  7. Reduction to Master Integrals by Baikov’s Method

    • Vladimir A. Smirnov
    Pages 139-172

  8. Evaluation by Differential Equations

    • Vladimir A. Smirnov
    Pages 173-184

  9. Tables

    • Vladimir A. Smirnov
    Pages 185-193

  10. Some Special Functions

    • Vladimir A. Smirnov
    Pages 195-197

  11. Summation Formulae

    • Vladimir A. Smirnov
    Pages 199-212

  12. Table of MB Integrals

    • Vladimir A. Smirnov
    Pages 213-226

  13. Analysis of Convergence and Sector Decompositions

    • Vladimir A. Smirnov
    Pages 227-238

  14. A Brief Review of Some Other Methods

    • Vladimir A. Smirnov
    Pages 239-249

  15. Applying Gröbner Bases to Solve IBP Relations

    • Vladimir A. Smirnov
    Pages 251-262

  16. Solutions

    • Vladimir A. Smirnov
    Pages 263-275

  17. Back Matter

    Pages 277-285
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Keywords

About this book

This is a textbook version of my previous book [190]. Problems and solutions have been included, Appendix G has been added, more details have been presented, recent publications on evaluating Feynman integrals have been taken into account and the bibliography has been updated. 1 ThegoalofthebookistodescribeindetailhowFeynmanintegrals canbe evaluatedanalytically.TheproblemofevaluatingLorentz-covariantFeynman integrals over loop momenta originated in the early days of perturbative quantum ?eld theory. Over a span of more than ?fty years, a great variety of methodsforevaluatingFeynmanintegralshasbeendeveloped.Mostpowerful modern methods are described in this book. Iunderstandthatifanotherperson–inparticularoneactivelyinvolvedin developing methods for Feynman integral evaluation – wrote a book on this subject, he or she would probably concentrate on some other methods and would rank the methods as most important and less important in a di?erent order. I believe, however, that my choice is reasonable. At least I have tried to concentrate on the methods that have been used recently in the most sophisticated calculations, in which world records in the Feynman integral ‘sport’ were achieved.

Reviews

From the reviews:

"The book is based on the courses of lectures given by the author in the two winter semesters of 2003-2004 and 2005-2006 at the University of Hamburg as a DFG Mercator professor in Hamburg as well as on the course given in 2003-2004 at the University of Karlsruhe. It will be useful for postgraduate students and theoretical physicists specializing in quantum field theory." (Michael B. Mensky, Zentralblatt MATH, Vol. 1111 (8), 2007)

Authors and Affiliations

  • Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia

    Vladimir A. Smirnov

Bibliographic Information

  • Book Title: Feynman Integral Calculus

  • Authors: Vladimir A. Smirnov

  • DOI: https://doi.org/10.1007/3-540-30611-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2006

  • Hardcover ISBN: 978-3-540-30610-8Published: 02 August 2006

  • Softcover ISBN: 978-3-642-06789-1Published: 14 October 2010

  • eBook ISBN: 978-3-540-30611-5Published: 15 November 2006

  • Edition Number: 1

  • Number of Pages: X, 287

  • Number of Illustrations: 52 b/w illustrations

  • Topics: Elementary Particles, Quantum Field Theory, Analysis, Quantum Physics

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