Feynman Integral Calculus by Vladimir A. Smirnov (2006, Hardcover)

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About this product

Product Identifiers

PublisherSpringer Berlin / Heidelberg

ISBN-103540306102

ISBN-139783540306108

eBay Product ID (ePID)54253187

Product Key Features

Number of PagesX, 287 Pages

LanguageEnglish

Publication NameFeynman Integral Calculus

SubjectPhysics / Quantum Theory, Calculus, Mathematical Analysis

Publication Year2006

TypeTextbook

Subject AreaMathematics, Science

AuthorVladimir A. Smirnov

FormatHardcover

Dimensions

Item Weight21.8 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2006-927416

ReviewsFrom 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), 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)

Number of Volumes1 vol.

IllustratedYes

Dewey DecimalPBKB

Table Of ContentFeynman 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.

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., 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. This is a textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author. 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. The book characterizes the most powerful methods and illustrates them with numerous examples, starting from very simple ones and progressing to nontrivial examples. Feynman Integral Calculus explains how the problem of evaluation has become ever more important since what could be easily evaluated has already been evaluated years ago. It demonstrates and explains how to perform the newest important calculations, while showing how to choose adequate methods and combine evaluation methods in a non-trivial way., 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., 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., 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.

LC Classification NumberQC793-793.5