Feynman Integral Calculus
Springer Berlin (Verlag)
978-3-642-06789-1 (ISBN)
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.
Feynman 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.
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)
| Erscheint lt. Verlag | 14.10.2010 |
|---|---|
| Zusatzinfo | X, 287 p. 52 illus. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 454 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik | |
| Naturwissenschaften ► Physik / Astronomie ► Hochenergiephysik / Teilchenphysik | |
| Naturwissenschaften ► Physik / Astronomie ► Quantenphysik | |
| Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
| Schlagworte | Alpha and Feynman parameters • Analysis • Baikov's Method • Calculus • differential equation • Dimensional regularization • Feynman integrals • Master Integral • Mellin-Barnes representation |
| ISBN-10 | 3-642-06789-1 / 3642067891 |
| ISBN-13 | 978-3-642-06789-1 / 9783642067891 |
| Zustand | Neuware |
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