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Renormalization Group and Fixed Points by Timothy J Hollowood Pdf
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.
Scaling and Renormalization in Statistical Physics by John Cardy Pdf
This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. It begins with a brief review of phase transitions in simple systems, then goes on to introduce the core ideas of the renormalisation group.
Lectures On Phase Transitions And The Renormalization Group by Nigel Goldenfeld Pdf
Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.
Introduction to the Functional Renormalization Group by Peter Kopietz,Lorenz Bartosch,Florian Schütz Pdf
This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics.
Richard J. Creswick,Horacio A. Farach,Charles P. Poole
Author : Richard J. Creswick,Horacio A. Farach,Charles P. Poole Publisher : Wiley-Interscience Page : 432 pages File Size : 49,9 Mb Release : 1992 Category : Science ISBN : UOM:39076001138036
Introduction to Renormalization Group Methods in Physics by Richard J. Creswick,Horacio A. Farach,Charles P. Poole Pdf
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.
Elements of Phase Transitions and Critical Phenomena by Hidetoshi Nishimori,Gerardo Ortiz Pdf
As an introductory account of the theory of phase transitions and critical phenomena, this book reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field. Most parts are written as self-contained units and every new concept or calculation is explained in detail without assuming prior knowledge of the subject. The book significantly enhances and revises a Japanese version which is a bestseller in the Japanese market and is considered a standard textbook in the field. It contains new pedagogical presentations of field theory methods, including a chapter on conformal field theory, and various modern developments hard to find in a single textbook on phase transitions. Exercises are presented as the topics develop, with solutions found at the end of the book, making the text useful for self-teaching, as well as for classroom learning.
Renormalization Group '91 by D V Shirkov,V B Priezzhev Pdf
The papers included here deal with the many faces of renormalization group formalism as it is used in different branches of theoretical physics. The subjects covered emphasize various applications to the theory of turbulence, chaos, quantum chaos in dynamical systems, spin systems and vector models. Also discussed are applications to related topics such as quantum field theory and chromodynamics, high temperature superconductivity and plasma physics. Contents:RG in Chern-Simons Field Theories and High-temperature Superconductivity (L V Avdeev & D I Kazakov)The Three-Loop QED Photon Vacuum Polarization Function in the MS-Scheme and the Four-Loop QED β-Function in the On-Shell Scheme (S G Gorishny et al)Method of Effective Charges and Brodsky-Lepage-MacKenzie Criterion (G Grunberg)Critical Exponents for Ising-Like Systems in Non-Integer Dimensions from Field Theory (Yu Holovatch & M Shpot)Scaling in Superconductors: Three-loop RG Expansions for a Three-Dimensional Model with Three Coupling Constants (S A Antonenko & A I Sokolov)A Renormalization Group Analysis of Frustrated Non-Collinear Magnets (P Azaria & B Delamotte)Critical Properties of the N-Vector Model Near Large-Scale Defects (R Z Bariev && I Z Ilaldinov)Dynamics of the Inhomogeneous Excitations in the One-Dimensional Isotropic X-Y Model of Spin s=1/2 (G O Berim)The Principle of Maximal Randomness in the Theory of Fully Developed Turbulence (L Ts Adzhemyan & M Yu Nalimov)Chaotic Renormalization Group Transformations (P H Damagaard)Symmetry Breaking Bifurcations in Chaotic Systems (P Grassberger & A S Pikovsky)The Renormalization Group Method Based on Group Analysis (V F Kovalev et al)and other papers Readership: Theoretical, statistical, mathematical and nuclear physics. keywords:
An Introduction To Quantum Field Theory, Student Economy Edition by Michael Peskin Pdf
An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.
Exact Renormalization Group, The - Proceedings Of The Workshop by Alexander Krasnitz,Yuri A Kubyshin,Robertus Potting,P Sa Pdf
The subject of the exact renormalization group started from pioneering work by Wegner and Houghton in the early seventies and, a decade later, by Polchinski, who formulated the Wilson renormalization group for field theory. In the past decade considerable progress has been made in this field, which includes the development of alternative formulations of the approach and of powerful techniques for solving the exact renormalization group equations, as well as widening of the scope of the exact renormalization group method to include fermions and gauge fields. In particular, two very recent results, namely the manifestly gauge-invariant formulation of the exact renormalization group equation and the proof of the c-theorem in four dimensions, are presented in this volume.
Field Theory, The Renormalization Group And Critical Phenomena (2nd Edition) by Daniel J Amit Pdf
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.
Renormalization Group by Giuseppe Benfatto,Giovanni Gallavotti Pdf
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.
Field Theory, The Renormalization Group, And Critical Phenomena: Graphs To Computers (3rd Edition) by Daniel J Amit,Victor Martin-mayor Pdf
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
