000 03568nam a22004815i 4500
001 978-3-642-34886-0
003 DE-He213
005 20140220083330.0
007 cr nn 008mamaa
008 130125s2012 gw | s |||| 0|eng d
020 _a9783642348860
_9978-3-642-34886-0
024 7 _a10.1007/978-3-642-34886-0
_2doi
050 4 _aQC770-798
072 7 _aPHP
_2bicssc
072 7 _aSCI051000
_2bisacsh
082 0 4 _a539.7
_223
100 1 _aSmirnov, Vladimir A.
_eauthor.
245 1 0 _aAnalytic Tools for Feynman Integrals
_h[electronic resource] /
_cby Vladimir A. Smirnov.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2012.
300 _aIX, 296 p. 63 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Tracts in Modern Physics,
_x0081-3869 ;
_v250
505 0 _aIntroduction -- 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.
520 _aThe 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.
650 0 _aPhysics.
650 0 _aField theory (Physics).
650 0 _aQuantum theory.
650 1 4 _aPhysics.
650 2 4 _aParticle and Nuclear Physics.
650 2 4 _aQuantum Physics.
650 2 4 _aField Theory and Polynomials.
650 2 4 _aNumerical and Computational Physics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642348853
830 0 _aSpringer Tracts in Modern Physics,
_x0081-3869 ;
_v250
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-34886-0
912 _aZDB-2-PHA
999 _c103808
_d103808