Renormalization Methods
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Renormalization Methods
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Author : Annick Lesne
language : en
Publisher: Wiley
Release Date : 1998-05-08
Renormalization Methods written by Annick Lesne and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-08 with Mathematics categories.
Originally conceived some thirty years ago in the context ofquantum electrodynamics, renormalization methods have progressivelydeveloped into an indispensable analytical tool used in widelyvarying domains of physics and applied mathematics, such as * phase transitions and critical phenomena * dynamical systems and chaos * developed turbulence * fractal structures and complex systems * percolation * polymer physics * diffusion in disordered media * measure theory and stochastic processes. By explaining the fundamental principles of renormalization theorysuch as scale invariance and universality which lie behind all thetechnical variations, this book aims to guide the reader to a moreunified understanding of today s physics. The book is based on avery accessible main text, supplemented by several more specializedsections; it is intended for graduate students and for researcherswho are seeking an introduction to a new area of electrodynamics ora general overview of the physical phenomena to whichrenormalization methods are applied.
Renormalization Methods
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Author : William David McComb
language : en
Publisher: OUP Oxford
Release Date : 2003-12-12
Renormalization Methods written by William David McComb and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-12 with Science categories.
This book is unique in occupying a gap between standard undergraduate texts and more advanced texts on quantum field theory. It covers a range of renormalization methods with a clear physical interpretation (and motivation), including mean-field theories and high-temperature and low-density expansions. It then proceeds by easy steps to the famous epsilon-expansion, ending up with the first-order corrections to critical exponents beyond mean-field theory. Nowadays there is widespread interest in applications of renormalization methods to various topics ranging over soft condensed matter, engineering dynamics, traffic queueing and fluctuations in the stock market. Hence macroscopic systems are also included, with particular emphasis on the archetypal problem of fluid turbulence. The book is also unique in making this material accessible to readers other than theoretical physicists, as it requires only the basic physics and mathematics which should be known to most scientists, engineers and mathematicians.
Renormalization Methods
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Author : William David McComb
language : en
Publisher: OUP Oxford
Release Date : 2007-11-15
Renormalization Methods written by William David McComb and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-15 with Science categories.
There is currently widespread interest in applications of renormalization methods to various topics ranging from fluid turbulence to fluctuations in the stock market. This book is unique in demystifying this material for non-specialists.
Introduction To Renormalization Group Methods In Physics
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Author : Richard J. Creswick
language : en
Publisher: Wiley-Interscience
Release Date : 1992
Introduction To Renormalization Group Methods In Physics written by Richard J. Creswick and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.
The renormalization group (RG) method has found applications in many areas of physics. The authors present simple RG treatments of such diverse problems as random walks, percolation, chaos and critical phenomena. Detailed introductory materials are presented in each area which makes it reasonably self–contained. The concepts of self–similarity and scale invariance are a common thread tying these problems together. Emphasis is placed on intuitive real–space RG calculations rather than formalism. The momentum–space RG is introduced and the 1/n and epsis expansions are discussed. A brief explanation of the field–theoretic approach to the RG serves as an introduction to more advanced techniques.
Introduction To A Renormalisation Group Method
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Author : Roland Bauerschmidt
language : en
Publisher: Springer Nature
Release Date : 2019-10-16
Introduction To A Renormalisation Group Method written by Roland Bauerschmidt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-16 with Science categories.
This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem. It also provides an overview of fundamental models in statistical mechanics with critical behaviour, including the Ising and φ4 models and the self-avoiding walk. The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry. Including exercises in each chapter to help readers deepen their understanding, it is a valuable resource for mathematicians and mathematical physicists wanting to learn renormalisation group theory.
Field Theory The Renormalization Group And Critical Phenomena Graphs To Computers 3rd Edition
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Author : Daniel J Amit
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-06-21
Field Theory The Renormalization Group And Critical Phenomena Graphs To Computers 3rd Edition written by Daniel J Amit and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-21 with Science categories.
This volume links field theory methods and concepts from particle physics with those in critical phenomena and statistical mechanics, the development starting from the latter point of view. Rigor and lengthy proofs are trimmed by using the phenomenological framework of graphs, power counting, etc., and field theoretic methods with emphasis on renormalization group techniques. Non-perturbative methods and numerical simulations are introduced in this new edition. Abundant references to research literature complement this matter-of-fact approach. The book introduces quantum field theory to those already grounded in the concepts of statistical mechanics and advanced quantum theory, with sufficient exercises in each chapter for use as a textbook in a one-semester graduate course.The following new chapters are included:I. Real Space MethodsII. Finite Size ScalingIII. Monte Carlo Methods. Numerical Field Theory
Renormalization Group
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Author : Giuseppe Benfatto
language : en
Publisher: Princeton University Press
Release Date : 2020-11-10
Renormalization Group written by Giuseppe Benfatto and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-10 with Science categories.
Scaling and self-similarity ideas and methods in theoretical physics have, in the last twenty-five years, coalesced into renormalization-group methods. This book analyzes, from a single perspective, some of the most important applications: the critical-point theory in classical statistical mechanics, the scalar quantum field theories in two and three space-time dimensions, and Tomonaga's theory of the ground state of one-dimensional Fermi systems. The dimension dependence is discussed together with the related existence of anomalies (in Tomonaga's theory and in 4 -e dimensions for the critical point). The theory of Bose condensation at zero temperature in three space dimensions is also considered. Attention is focused on results that can in principle be formally established from a mathematical point of view. The 4 -e dimensions theory, Bose condensation, as well as a few other statements are exceptions to this rule, because no complete treatment is yet available. However, the truly mathematical details are intentionally omitted and only referred to. This is done with the purpose of stressing the unifying conceptual structure rather than the technical differences or subtleties.
Tensorial Methods And Renormalization In Group Field Theories
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Author : Sylvain Carrozza
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-04-12
Tensorial Methods And Renormalization In Group Field Theories written by Sylvain Carrozza 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 2014-04-12 with Science categories.
The main focus of this thesis is the mathematical structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related, on the one hand, to Loop Quantum Gravity (LQG) and on the other, to matrix- and tensor models. Background material on these topics, including conceptual and technical aspects, are introduced in the first chapters. The work then goes on to explain how the standard tools of Quantum Field Theory can be generalized to GFTs and exploited to study the large cut-off behaviour and renormalization group transformations of the latter. Among the new results derived in this context are a proof of renormalizability of a three-dimensional GFT with gauge group SU(2), which opens the way to applications of the formalism to quantum gravity.
Introduction To The Functional Renormalization Group
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Author : Peter Kopietz
language : en
Publisher: Springer
Release Date : 2010-04-22
Introduction To The Functional Renormalization Group written by Peter Kopietz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-22 with Science categories.
The renormalization group (RG) has nowadays achieved the status of a meta-theory, which is a theory about theories. The theory of the RG consists of a set of concepts and methods which can be used to understand phenomena in many different ?elds of physics, ranging from quantum ?eld theory over classical statistical mechanics to nonequilibrium phenomena. RG methods are particularly useful to understand phenomena where ?uctuations involving many different length or time scales lead to the emergence of new collective behavior in complex many-body systems. In view of the diversity of ?elds where RG methods have been successfully applied, it is not surprising that a variety of apparently different implementations of the RG idea have been proposed. Unfortunately, this makes it somewhat dif?cult for beginners to learn this technique. For example, the ?eld-theoretical formulation of the RG idea looks at the ?rst sight rather different from the RG approach pioneered by Wilson, the latter being based on the concept of the effective action which is ite- tively calculated by successive elimination of the high-energy degrees of freedom. Moreover, the Wilsonian RG idea has been implemented in many different ways, depending on the particular problem at hand, and there seems to be no canonical way of setting up the RG procedure for a given problem.
Field Theory The Renormalization Group And Critical Phenomena 2nd Edition
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Author : Daniel J Amit
language : en
Publisher: World Scientific Publishing Company
Release Date : 1984-08-31
Field Theory The Renormalization Group And Critical Phenomena 2nd Edition written by Daniel J Amit and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-08-31 with categories.
This volume links field theory methods and concepts from particle physics with those in critical phenomena and statistical mechanics, the development starting from the latter point of view. Rigor and lengthy proofs are trimmed by using the phenomenological framework of graphs, power counting, etc., and field theoretic methods with emphasis on renormalization group techniques. The book introduces quantum field theory to those already grounded in the concepts of statistical mechanics and advanced quantum theory, with sufficient exercises in each chapter for use as a textbook in a one-semester graduate course.