Evaluating Feynman Integrals

1. Auflage 2004
ISBN: 978-3-540-23933-8
Verlag: Springer

Buch, Englisch, Band 211, 250 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1220 g

Reihe: Springer Tracts in Modern Physics

The problem of evaluating Feynman integrals over loop momenta has existed from the early days of perturbative quantum field theory.

Although a great variety of methods for evaluating Feynman integrals has been developed over a span of more than fifty years, this book is a first attempt to summarize them. Evaluating Feynman Integrals characterizes the most powerful methods, in particular those used for recent, quite sophisticated calculations, and then illustrates them with numerous examples, starting from very simple ones and progressing to nontrivial examples.

Zielgruppe

Research

Autoren/Hrsg.

Smirnov, Vladimir A.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

Introduction.- Feynman Integrals: Basic Definitions and Tools.- Evaluating by Alpha and Feynman Parameters.- Evaluating by Mellin-Barnes Representation.- IBP and Reduction to Master Integrals.- Reduction to Master Integrals by Baikov's method.- Evaluation by Differential Equations.- Appendix A. Tables.- Appendix B. Some Special Functions.- Appendix C. Summation Formulae.- Appendix D. Table of MB Integrals.- Appendix E. Analysis of Convergence and Sector Decompositions.- Appendix F. A Brief Review of Some Other Methods.