Introduction to Renormalization Group Methods in Physics PDF Download

Author: R. J. Creswick
Publisher:
ISBN: 9780486793450
Category : Renormalization (Physics)
Languages : en
Pages : 0

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Book Description
This introduction to the renormalization group, an edited and corrected second edition, discusses examples from diverse areas of physics. Designed for a one-semester course for advanced graduate students, the treatment requires a solid background in classical mechanics, statistical mechanics, and quantum mechanics. The text begins with an examination of self-similarity and scale invariance, followed by chapters on the renormalization group approaches to chaos and percolation, renormalization group and critical phenomena, and an extensive treatment of the Ising model. Additional topics include mean field theory and the Gaussian fixed point, the spherical model and the 1/n expansion, the two-dimensional X-Y model and the Kosterlitz-Thouless transition, and other subjects. Each chapter is augmented by problems and references, and three helpful Appendixes supplement the text. AUTHOR: R. J. Creswick is Professor in the Department of Physics and Astronomy, University of South Carolina.

Author: Annick Lesne
Publisher: Wiley
ISBN: 9780471966890
Category : Mathematics
Languages : en
Pages : 0

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Book Description
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.

Author: W. D. McComb
Publisher: Oxford University Press
ISBN: 0198506945
Category : Business & Economics
Languages : en
Pages : 349

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Book Description
This text fills a gap between undergraduate and more advanced texts on quantum field theory. It covers a range of renormalization methods with a clear physical interpretation, proceeds to the epsilon-expansion and ends with the first-order corrections to critical exponents beyond mean-field theory.

Author: Roland Bauerschmidt
Publisher: Springer Nature
ISBN: 9813295937
Category : Science
Languages : en
Pages : 283

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Book Description
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.

Author: William David McComb
Publisher: OUP Oxford
ISBN: 019156723X
Category : Science
Languages : en
Pages : 348

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Book Description
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.

Author: Achim Schwenk
Publisher: Springer
ISBN: 3642273203
Category : Science
Languages : en
Pages : 356

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Book Description
There have been many recent and important developments based on effective field theory and the renormalization group in atomic, condensed matter, nuclear and high-energy physics. These powerful and versatile methods provide novel approaches to study complex and strongly interacting many-body systems in a controlled manner. The six extensive lectures gathered in this volume combine selected introductory and interdisciplinary presentations focused on recent applications of effective field theory and the renormalization group to many-body problems in such diverse fields as BEC, DFT, extreme matter, Fermi-liquid theory and gauge theories. Primarily aimed at graduate students and junior researchers, they offer an opportunity to explore fundamental physics across subfield boundaries at an early stage in their careers.

Author: Daniel J Amit
Publisher: World Scientific Publishing Company
ISBN: 9813104147
Category :
Languages : en
Pages : 412

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Book Description
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.

Author: Manfred Salmhofer
Publisher: Springer Science & Business Media
ISBN: 3662038730
Category : Science
Languages : en
Pages : 241

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Book Description
This monograph is the first to present the recently discovered renormalization techniques for the Schrödinger and Dirac equations, providing a mathematically rigorous, yet simple and clear introduction to the subject. It develops field-theoretic techniques such as Feynman graph expansions and renormalization, taking pains to make all proofs as simple as possible by using generating function techniques throughout. Renormalization is performed by using an exact renormalization group differential equation, a technique that provides simple but complete proofs of the theorems.

Author: Richard J. Creswick
Publisher: Wiley-Interscience
ISBN:
Category : Science
Languages : en
Pages : 432

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Book Description
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.

Author: Timothy J Hollowood
Publisher: Springer Science & Business Media
ISBN: 3642363121
Category : Science
Languages : en
Pages : 78

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Book Description
This Brief presents an introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics. Emphasis is placed on gaining a physical understanding of the running of the couplings. The Wilsonian version of the renormalization group is related to conventional perturbative calculations with dimensional regularization and minimal subtraction. An introduction is given to some of the remarkable renormalization group properties of supersymmetric theories.