Evaluating Feynman Integrals

Vladimir Smirnov (auth.)9783540239338, 3-540-23933-2

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.

Table of contents :
Introduction….Pages 1-9
Feynman Integrals: Basic Definitions and Tools….Pages 11-30
Evaluating by Alpha and Feynman Parameters….Pages 31-53
Evaluating by MB Representation….Pages 55-107
IBP and Reduction to Master Integrals….Pages 109-132
Reduction to Master Integrals by Baikov’s Method….Pages 133-163
Evaluation by Differential Equations….Pages 165-177
Tables….Pages 179-186
Some Special Functions….Pages 187-190
Summation Formulae….Pages 191-205
Table of MB Integrals….Pages 207-219
Analysis of Convergence and Sector Decompositions….Pages 221-232
A Brief Review of Some Other Methods….Pages 233-244