Applied Asymptotic Expansions in Momenta and Masses

Applied Asymptotic Expansions in Momenta and Masses PDF

Author: Vladimir A. Smirnov

Publisher: Springer

Published: 2003-07-01

Total Pages: 270

ISBN-13: 3540445749

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'The sturgeon they sent was second grade fresh,' said the barman. 'Really, what nonsense/' 'Why nonsense?' '"Second grade fresh" that's what I call nonsense/ There's only one degree of freshness the first, and it's the last) (M. A. Bulgakov, The Master and Margarita) The goal of this book is to describe in detail how Feynman integrals can be expanded in suitable parameters, when various momenta or masses are small or large. In a narrow sense, this problem is connected with practical calcula tions. In a situation where a given Feynman integral depends on parameters of very different scales, a natural idea is to replace it by a sufficiently large number of terms of an expansion of it in ratios of small and large scales. It will be explained how this problem of expansion can be systematically solved, by formulating universal prescriptions that express terms of the expansion by using the original Feynman integral with its integrand expanded into a Taylor series in appropriate momenta and masses. It turns out that knowledge of the structure of the asymptotic expansion at the diagrammatic level is a key point in understanding how to perform expansions at the operator level. There are various examples of these ex pansions: the operator product expansion, the large mass expansion, Heavy Quark Effective Theory, Non Relativistic QCD, etc. Each of them serves as a realization of the factorization of contributions of different scales.

Analytic Tools for Feynman Integrals

Analytic Tools for Feynman Integrals PDF

Author: Vladimir A. Smirnov

Publisher: Springer

Published: 2013-01-15

Total Pages: 298

ISBN-13: 9783642348877

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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.

Analytic Tools for Feynman Integrals

Analytic Tools for Feynman Integrals PDF

Author: Vladimir A. Smirnov

Publisher: Springer

Published: 2013-01-16

Total Pages: 299

ISBN-13: 3642348866

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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.

Radiative Corrections, Radcor 98: Application Of Quantum Field Theory To Phenomenology - Proceedings Of 4th

Radiative Corrections, Radcor 98: Application Of Quantum Field Theory To Phenomenology - Proceedings Of 4th PDF

Author: Joan Sola

Publisher: World Scientific

Published: 1999-09-17

Total Pages: 606

ISBN-13: 9814543713

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This volume contains the contributions of 47 leading researchers in high energy physics, both theorists and experimentalists, from all over the world. It discusses the application of quantum field theory to phenomenology in all areas of active research in particle physics. The topics covered include: (i) the status of precision measurements at LEP, SLC, HERA, Tevatron, and other experiments; (ii) quantum-field-theoretical techniques for calculating electroweak and QCD radiative corrections; and (iii) radiative corrections and precision experiments in future colliders (Tevatron II, LHC, NLC, Muon Collider, etc.). The confrontation in a single volume of all the high precision results reported by experimentalists, on one side, with the predictions of the Standard Model (SM) at the level of radiative corrections, on the otherside, provides a detailed test of the SM at the quantum level. And, where discrepancies appear, it gives hints of physics beyond the SM (such as supersymmetry, effective quantum field theories, etc.) which are thoroughly discussed in the book.

High Performance Computing in Science and Engineering ́15

High Performance Computing in Science and Engineering ́15 PDF

Author: Wolfgang E. Nagel

Publisher: Springer

Published: 2016-02-05

Total Pages: 701

ISBN-13: 331924633X

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This book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2015. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe’s leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance. The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.

Neutrino Mass

Neutrino Mass PDF

Author: Guido Altarelli

Publisher: Springer Science & Business Media

Published: 2003-09-08

Total Pages: 272

ISBN-13: 9783540403289

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Reviews the current state of knowledge of neutrino masses and the related question of neutrino oscillations. After an overview of the theory of neutrino masses and mixings, detailed accounts are given of the laboratory limits on neutrino masses, astrophysical and cosmological constraints on those masses, experimental results on neutrino oscillations, the theoretical interpretation of those results, and theoretical models of neutrino masses and mixings. The book concludes with an examination of the potential of long-baseline experiments. This is an essential reference text for workers in elementary-particle physics, nuclear physics, and astrophysics.

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