Download or read book Applied Asymptotic Expansions in Momenta and Masses written by Vladimir A. Smirnov and published by Springer. This book was released on 2003-07-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.
Download or read book Applied Asymptotic Expansions in Momenta and Masses written by Vladimir A. Smirnov and published by Springer. This book was released on 2014-03-12 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.
Download or read book Applied Asymptotic Expansions in Momenta and Masses written by Vladimir A. Smirnov and published by Springer Science & Business Media. This book was released on 2001-11-06 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.
Download or read book Neutrino Mass written by Guido Altarelli and published by Springer Science & Business Media. This book was released on 2003-09-08 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Analytic Tools for Feynman Integrals written by Vladimir A. Smirnov and published by Springer. This book was released on 2013-01-16 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Soft Collinear Effective Theory written by Thomas Becher and published by Springer. This book was released on 2015-03-04 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among resummation techniques for perturbative QCD in the context of collider and flavor physics, soft-collinear effective theory (SCET) has emerged as both a powerful and versatile tool, having been applied to a large variety of processes, from B-meson decays to jet production at the LHC. This book provides a concise, pedagogical introduction to this technique. It discusses the expansion of Feynman diagrams around the high-energy limit, followed by the explicit construction of the effective Lagrangian - first for a scalar theory, then for QCD. The underlying concepts are illustrated with the quark vector form factor at large momentum transfer, and the formalism is applied to compute soft-gluon resummation and to perform transverse-momentum resummation for the Drell-Yan process utilizing renormalization group evolution in SCET. Finally, the infrared structure of n-point gauge-theory amplitudes is analyzed by relating them to effective-theory operators. This text is suitable for graduate students and non-specialist researchers alike as it requires only basic knowledge of perturbative QCD.
Download or read book Anti Differentiation and the Calculation of Feynman Amplitudes written by Johannes Blümlein and published by Springer Nature. This book was released on 2021-11-26 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews. The book aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.
Download or read book Evaluating Feynman Integrals written by Vladimir A. Smirnov and published by Springer. This book was released on 2005-02-28 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Feynman Integral Calculus written by Vladimir A. Smirnov and published by Springer Science & Business Media. This book was released on 2006-11-15 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Control Theory in Physics and Other Fields of Science written by Michael Schulz and published by Springer Science & Business Media. This book was released on 2006-01-13 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers systematically and in a simple language the mathematical and physical foundations of controlling deterministic and stochastic evolutionary processes in systems with a high degree of complexity. Strong emphasis is placed on concepts, methods and techniques for modelling, assessment and the solution or estimation of control problems in an attempt to understand the large variability of these problems in several branches of physics, chemistry and biology as well as in technology and economics. The main focus of the book is on a clear physical and mathematical understanding of the dynamics and kinetics behind several kinds of control problems and their relation to self-organizing principles in complex systems. The book is a modern introduction and a helpful tool for researchers, engineers as well as post-docs and graduate students interested in an application oriented control theory and related topics.
Download or read book A Primer for Chiral Perturbation Theory written by Stefan Scherer and published by Springer. This book was released on 2011-10-01 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques.
Download or read book Cosmology written by Dierck-Ekkehard Liebscher and published by Springer Science & Business Media. This book was released on 2005-04-20 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cosmology deals with the current state of thinking about the basic questions at the center of the field of cosmology. More emphasis than usual is put on the connections to related domains of science, such as geometry, relativity, thermodynamics, particle physics, and - in particular - on the intrinsic connections between the different topics. The chapters are illustrated with many figures that are as exact as currently possible, e.g. in the case of geometry and relativity. Readers acquire a graduate-level knowledge of cosmology as it is required to understand the cosmological impact of their particular research topics, as well as an introduction into the current research in the field.
Download or read book Theory of the Muon Anomalous Magnetic Moment written by Kirill Melnikov and published by Springer. This book was released on 2007-01-09 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of the muon anomalous magnetic moment is particle physics in a nutshell. It is an interesting, exciting and difficult subject, and this book provides a comprehensive review of it. The theory of the muon anomalous magnetic moment is at the cutting edge of current research in particle physics, and any deviation between the theoretical prediction and the experimental value might be interpreted as a signal of an as-yet-unknown new physics.
Download or read book Spinning Particles Semiclassics and Spectral Statistics written by Stefan Keppeler and published by Springer Science & Business Media. This book was released on 2003-09-11 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is semiclassical methods for systems with spin, in particular methods involving trace formulae and torus quantisation and their applications in the theory of quantum chaos, e.g. the characterisation of spectral correlations. The theoretical tools developed here not only have immediate applications in the theory of quantum chaos - which is the second focus of the book - but also in atomic and mesoscopic physics. Thus the intuitive understanding of semiclassical spin dynamics will also be helpful in emerging subjects like spintronics and quantum computation.
Download or read book Inelastic Light Scattering of Semiconductor Nanostructures written by Christian Schüller and published by Springer Science & Business Media. This book was released on 2006-09-14 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of semiconductor nanostructures is of enormous and still-growing research interest. On one hand, they are already realized in mass products such as high-electron-mobility field-effect transistors and quantum-well lasers. On the other hand, they allow, in specially tailored systems, the investigation of fundamental properties such as many-particle interactions of electrons in reduced dimensions. This book bridges the gap between general semiconductor textbooks and research articles.
Download or read book The Flow Equation Approach to Many Particle Systems written by Stefan Kehrein and published by Springer. This book was released on 2007-01-09 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained introduction addresses the novel flow equation approach for many particle systems and provides an up-to-date review of the subject. The text first discusses the general ideas and concepts of the flow equation method, and then in a second part illustrates them with various applications in condensed matter theory. The third and last part of the book contains an outlook with current perspectives for future research.
Download or read book Spin orbit Coupling Effects in Two Dimensional Electron and Hole Systems written by Roland Winkler and published by Springer. This book was released on 2003-10-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part provides a general introduction to the electronic structure of quasi-two-dimensional systems with a particular focus on group-theoretical methods. The main part of the monograph is devoted to spin-orbit coupling phenomena at zero and nonzero magnetic fields. Throughout the book, the main focus is on a thorough discussion of the physical ideas and a detailed interpretation of the results. Accurate numerical calculations are complemented by simple and transparent analytical models that capture the important physics.
