Feynman Integral Calculus
Edition: 1 edition
Publisher: Springer
Published: September 14, 2006
Language: eng
Format: Hardcover
Number of pages: 287
ISBN-13: 9783540306108
Subjects: Calculus & mathematical analysis; Quantum Theory; Mathematics; Science; Science/Mathematics; Mathematical Analysis; Nuclear Physics; Alpha and Feynman parameters; Baikov's Method; Dimensional regularization; Feynman integrals; Master Integral; Mellin-Barnes representation; Science / Nuclear Physics; Calculus
First sentence: The important mathematical problem of evaluating Feynman integrals arises quite naturally in elementary-particle physics when one treats various quantities in the framework of perturbation theory.
Description: The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and illustrates them with numerous examples starting from very simple ones and progressing to nontrivial examples. The book demonstrates how to choose adequate methods and combine evaluation methods in a non-trivial way. The most powerful methods are characterized and then illustrated through numerous examples. This is an updated textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author.
Table of contents: title: Introduction.; title: Feynman Integrals: Basic Definitions and Tools.; title: Evaluating by Alpha and Feynman Parameters.; title: Evaluating by MB Representation.; title: IBP and Reduction to Master Integrals.; title: Reduction to Master Integrals by Baikov's Method.; title: Evaluating by Differential Equations.; title: Appendix A: Tables.; title: Appendix B: Some Special Functions.; title: Appendix C: Summation Formulae.; title: Appendix D: Table of MB integrals.; title: Appendix E: Analysis of Convergence and Sector Decompositions.; title: Appendix F: A brief Review of some other Methods.; title: Appendix G: Applying Gröbner Bases to Solve IBP Relations.- Solutions.