Evaluating Feynman Integrals
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Evaluating Feynman Integrals
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Author : Vladimir A. Smirnov
language : en
Publisher: Springer
Release Date : 2005-02-28
Evaluating Feynman Integrals written by Vladimir A. Smirnov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-28 with Science categories.
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.
Feynman Integral Calculus
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Author : Vladimir A. Smirnov
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-02
Feynman Integral Calculus written by Vladimir A. Smirnov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-02 with Mathematics categories.
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. The book characterizes the most powerful methods and illustrates them with numerous examples starting from very simple ones and progressing to nontrivial examples. The book demonstrates how to choose adequate methods and combine evaluation methods in a non-trivial way. The most powerful methods are characterized and then illustrated through numerous examples. This is an updated textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author.
Analytic Tools For Feynman Integrals
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Author : Vladimir A. Smirnov
language : en
Publisher: Springer
Release Date : 2013-01-16
Analytic Tools For Feynman Integrals written by Vladimir A. Smirnov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-16 with Science categories.
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.
Finding New Relationships Between Hypergeometric Functions By Evaluating Feynman Integrals
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Author : Bernd A. Kniehl
language : en
Publisher:
Release Date : 2011
Finding New Relationships Between Hypergeometric Functions By Evaluating Feynman Integrals written by Bernd A. Kniehl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
Quantum Mechanical Calculations Based On Evaluating Feynman Path Integrals By The Monte Carlo Method
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Author : Dave Arthur Campbell
language : en
Publisher:
Release Date : 1975
Quantum Mechanical Calculations Based On Evaluating Feynman Path Integrals By The Monte Carlo Method written by Dave Arthur Campbell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Feynman integrals categories.
Feynman Motives
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Author : Matilde Marcolli
language : en
Publisher: World Scientific
Release Date : 2010
Feynman Motives written by Matilde Marcolli and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.
This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. The main question is whether residues of Feynman integrals always evaluate to periods of mixed Tate motives, as appears to be the case from extensive computations of Feynman integrals carried out by Broadhurst and Kreimer. Two different approaches to the subject are described. The first, a "bottom-up" approach, constructs explicit algebraic varieties and periods from Feynman graphs and parametric Feynman integrals. This approach grew out of work of Bloch–Esnault–Kreimer and suggests that, while the algebraic varieties associated to the Feynman graphs can be arbitrarily complicated as motives, the part that is involved in the Feynman integral computation might still be of the special mixed Tate kind. A second, "top-down" approach to the problem, developed in the work of Connes and the author, consists of comparing a Tannakian category constructed out of the data of renormalization with those formed by mixed Tate motives. The book draws connections between these two approaches and gives an overview of various ongoing directions of research in the field. The text is aimed at researchers in mathematical physics, high energy physics, number theory and algebraic geometry. Based on lecture notes for a graduate course given by the author at Caltech in the fall of 2008, it cal also be used by graduate students interested in working in this area.
A New Method For Evaluating Two Loop Feynman Integrals And Its Application To Higgs Production
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Author : Stefan Beerli
language : en
Publisher:
Release Date : 2008
A New Method For Evaluating Two Loop Feynman Integrals And Its Application To Higgs Production written by Stefan Beerli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Monte Carlo Evaluation Of Feynman Path Integrals In Imaginary Time
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Author : Suresh Vencatesh Lawamie
language : en
Publisher:
Release Date : 1969
Monte Carlo Evaluation Of Feynman Path Integrals In Imaginary Time written by Suresh Vencatesh Lawamie and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Feynman integrals categories.
Homology And Feynman Integrals
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Author : Rudolph C. Hwa
language : en
Publisher:
Release Date : 1966
Homology And Feynman Integrals written by Rudolph C. Hwa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Mathematics categories.
Numerical Evaluation Of Tensor Feynman Integrals In Euclidean Kinematics
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Author :
language : en
Publisher:
Release Date : 2010
Numerical Evaluation Of Tensor Feynman Integrals In Euclidean Kinematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.