Description
Book SynopsisThe 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.
Trade ReviewFrom 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)
Table of ContentsFeynman Integrals: Basic Definitions and Tools.- Evaluating by Alpha and Feynman Parameters.- Evaluating by MB Representation.- IBP and Reduction to Master Integrals.- Reduction to Master Integrals by Baikov’s Method.- Evaluation by Differential Equations.- Tables.- Some Special Functions.- Summation Formulae.- Table of MB Integrals.- Analysis of Convergence and Sector Decompositions.- A Brief Review of Some Other Methods.- Applying Gröbner Bases to Solve IBP Relations.- Solutions.
