Analytic Tools for Feynman Integrals

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint : Springer, 2012

Abstract/Sommario: Introduction -- Feynman Integrals: Basic Definitions and Tools.-Evaluating by Alpha and Feynman Parameters -- Sector Decompositions -- Evaluating by Mellin-Barnes Representation -- Integration by Parts and Reduction to Master Integrals -- Evaluation by Differential Equations -- Evaluating Master Integrals by Dimensional Recurrence and Analyticity -- Asymptotic Expansions in Momenta and Masses -- Tables -- Some Special Functions- Summation Formulae -- Table of MB Integrals.- A Brief Rev ...; [leggi tutto] Introduction -- Feynman Integrals: Basic Definitions and Tools.-Evaluating by Alpha and Feynman Parameters -- Sector Decompositions -- Evaluating by Mellin-Barnes Representation -- Integration by Parts and Reduction to Master Integrals -- Evaluation by Differential Equations -- Evaluating Master Integrals by Dimensional Recurrence and Analyticity -- Asymptotic Expansions in Momenta and Masses -- Tables -- Some Special Functions- Summation Formulae -- Table of MB Integrals.- A Brief Review of Some Other Methods. - The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice. This book supersedes the author’s previous Springer book “Evaluating Feynman Integrals” and its textbook version “Feynman Integral Calculus.” Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often public. In comparison to the two previous books, three new chapters have been added: One is on sector decomposition, while the second describes a new method by Lee. The third new chapter concerns the asymptotic expansions of Feynman integrals in momenta and masses, which were described in detail in another Springer book, “Applied Asymptotic Expansions in Momenta and Masses,” by the author. This chapter describes, on the basis of papers that appeared after the publication of said book, how to algorithmically discover the regions relevant to a given limit within the strategy of expansion by regions. In addition, the chapters on the method of Mellin-Barnes representation and on the method of integration by parts have been substantially rewritten, with an emphasis on the corresponding algorithms and computer codes [comprimi]

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Campo	Valore
Descrizione	Analytic Tools for Feynman Integrals / by Vladimir A. Smirnov. - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint : Springer, 2012. - IX, 296 p. 63 illus ; digital. - (Springer Tracts in Modern Physics ; 250)
Specifiche	[Supporto spec. Risorsa elettr.] Risorsa remota
Note	Springer eBooks. - Printed edition: 9783642348853
Collezione	[Fa parte di] Springer Tracts in Modern Physics ; 250 [Vai al dettaglio]
Autori	Smirnov, Vladimir A. - [Responsabilità principale] SpringerLink (Online service) - [Responsabilità secondaria]
Soggetto	Field theory (Physics) Field Theory and Polynomials Numerical and Computational Physics Particle and Nuclear Physics Physics Quantum Physics Quantum Theory
Classificazione	539.7 - Fisica atomica e nucleare
Lingua	Inglese
Numeri	ISBN: 978-3-642-34886-0 DOI: 10.1007/978-3-642-34886-0 N. catalogo straniero: QC770-798 (Library of Congress Call Number)
ID scheda	130118
Permalink	https://www.opac.inaf.it/?ids=130118