Renormalization Group Theory
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Author | : Timothy J Hollowood |
Publisher | : Springer Science & Business Media |
Total Pages | : 78 |
Release | : 2013-03-28 |
Genre | : Science |
ISBN | : 3642363121 |
Download Renormalization Group and Fixed Points Book in PDF, Epub and Kindle
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.
Author | : Ulrich Köbler |
Publisher | : Springer Science & Business Media |
Total Pages | : 402 |
Release | : 2010-04-29 |
Genre | : Technology & Engineering |
ISBN | : 3642024882 |
Download Renormalization Group Theory Book in PDF, Epub and Kindle
Spin wave theory of magnetism and BCS theory of superconductivity are typical theories of the time before renormalization group (RG) theory. The two theories consider atomistic interactions only and ignore the energy degrees of freedom of the continuous (infinite) solid. Since the pioneering work of Kenneth G. Wilson (Nobel Prize of physics in 1982) we know that the continuous solid is characterized by a particular symmetry: invariance with respect to transformations of the length scale. Associated with this symmetry are particular field particles with characteristic excitation spectra. In diamagnetic solids these are the well known Debye bosons. This book reviews experimental work on solid state physics of the last five decades and shows in a phenomenological way that the dynamics of ordered magnets and conventional superconductors is controlled by the field particles of the infinite solid and not by magnons and Cooper pairs, respectively. In the case of ordered magnets the relevant field particles are called GSW bosons after Goldstone, Salam and Weinberg and in the case of superconductors the relevant field particles are called SC bosons. One can imagine these bosons as magnetic density waves or charge density waves, respectively. Crossover from atomistic exchange interactions to the excitations of the infinite solid occurs because the GSW bosons have generally lower excitation energies than the atomistic magnons. According to the principle of relevance the dynamics is governed by the excitations with the lowest energy. The non relevant atomistic interactions with higher energy are practically unimportant for the dynamics.
Author | : Roland Bauerschmidt |
Publisher | : Springer Nature |
Total Pages | : 283 |
Release | : 2019-10-16 |
Genre | : Science |
ISBN | : 9813295937 |
Download Introduction to a Renormalisation Group Method Book in PDF, Epub and Kindle
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 | : Achim Schwenk |
Publisher | : Springer |
Total Pages | : 356 |
Release | : 2012-06-25 |
Genre | : Science |
ISBN | : 3642273203 |
Download Renormalization Group and Effective Field Theory Approaches to Many-Body Systems Book in PDF, Epub and Kindle
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 | : Giuseppe Benfatto |
Publisher | : Princeton University Press |
Total Pages | : 156 |
Release | : 1995-07-30 |
Genre | : Mathematics |
ISBN | : 9780691044460 |
Download Renormalization Group Book in PDF, Epub and Kindle
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.
Author | : Daniel J Amit |
Publisher | : World Scientific Publishing Company |
Total Pages | : 568 |
Release | : 2005-06-21 |
Genre | : Science |
ISBN | : 9813102071 |
Download Field Theory, The Renormalization Group, And Critical Phenomena: Graphs To Computers (3rd Edition) Book in PDF, Epub and Kindle
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
Author | : John C. Collins |
Publisher | : Cambridge University Press |
Total Pages | : 393 |
Release | : 2023-07-31 |
Genre | : Science |
ISBN | : 1009401769 |
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Author | : A.N. Vasil'ev |
Publisher | : CRC Press |
Total Pages | : 704 |
Release | : 2004-04-28 |
Genre | : Science |
ISBN | : 1134389663 |
Download The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics Book in PDF, Epub and Kindle
This volume provides a general field-theoretical picture of critical phenomena and stochastic dynamics and helps readers develop a practical skill for calculations. This education on the practical skill sets this book apart: it is the first to give a full technical introduction to the field. Both general ideas and ...hard... calculations are presen
Author | : Karl F. Freed |
Publisher | : Wiley-Interscience |
Total Pages | : 361 |
Release | : 1987-03-12 |
Genre | : Science |
ISBN | : 9780471828457 |
Download Renormalization Group Theory of Macromolecules Book in PDF, Epub and Kindle
Studies theory and application of long wave-length properties of polymers. Utilizes statistical mechanics and employs simple models in developing predictive statistical mechanical theories of polymers, which are of great practical interest in technological applications and in understanding the biological use of polymer molecules. Topics covered include configurational statistics of polymer chains, functional integration, flexible polymer chains, the excluded volume problem, scaling theory, renormalization group description of polymer extended volume, use of perturbation and epsilon-expansions in renormalization group treatment of polymers, and much more.
Author | : Daniel J Amit |
Publisher | : World Scientific Publishing Company |
Total Pages | : 412 |
Release | : 1984-08-31 |
Genre | : |
ISBN | : 9813104147 |
Download Field Theory, The Renormalization Group And Critical Phenomena (2nd Edition) Book in PDF, Epub and Kindle
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.