Book Description
Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics.
Customer Reviews:
Probably the best book on CFT.......2006-10-27
I have come across some books and lecture notes on CFT, but this book truly is great - almost all notes are based on this book. It presents elementary CFT at an understand pace and progresses slowly towards the end to the more advanced topics in 2D string theory and statistical physics.
The book is pleasant to read and the derivations are done well. Some minor errors and typos are forgiven, because the rest of the book makes well up for them. Numerous examples are given in each section and there are many problems at the end of each chapter. Unfortunately, there are no detailed solutions available, as far as I know.
Some prior knowledge of QFT might be useful, but the basics (Lagrangian formalism, Wick's theorem, Noether's theorem and conserved currents, etc.) are provided in the first chapters. This book is highly recommended for those interested in CFT and its application to string theory (and statistical physics), and I even dare to say it is a MUST!
This is a great book for beginners to learn CFT........1999-09-03
This book is really well done. It introduce the theory of conformal fields in a really pedagogical way so that any person not familiar at all with the subject can enjoy it. The review of quantum field theory and statistical mechanics at the begining is excellent and it is of great help if you haven't work with these subjects recently. The book is also filled with many basic applications that make the theory closer to real life.
Congratulations for this nice book!
A definite "must have" for those interested in CFT........1999-08-31
This book is a fine contribution to the literature on conformal field theory and will no doubt become one of the standard references on the subject. It is well worth the price as it gives a comprehensive introduction to the subject. Chapter 5 is a good discussion of local conformal invariance and clears up some of my own misunderstandings of this invariance. The later chapters discuss affine Lie algebras and algebraic considerations in detail.
Very complete, the reference in the field.......1999-04-27
Probably the best book to introduce you to conformal field theory. It starts from basics and go up to coset constrcutions, WZW models. More than a textbook, it is a necessary reference!
Book Description
String theory continues to progress at an astonishing rate, and this book brings the reader up to date with the latest developments and the most active areas of research in the field. Building on the foundations laid in his Introduction to Superstrings and M Theory, Professor Kaku discusses such topics as the classification of conformal string theories, knot theory, the Yang-Baxter relation, quantum groups, and the insights into 11-dimensional strings recently obtained from M-theory. New chapters discuss such topics as Seiberg- Witten theory, M theory and duality., and D-branes. Several chapters review the fundamentals of string theory, making the presentation of the material self-contained while keeping overlap with the earlier book to a minimum. This book conveys the vitality of the current research and places readers at its forefront.
Customer Reviews:
a fine supplement to standard textbooks .......2006-10-27
Like all books of Michio Kaku, the book is written nicely and the topics included are indeed modern and up to date. In order to understand it, it is recommended that one has done a course on superstring theory, preferably on infinite-dimensional Lie algebras and supersymmetry too, and that one has read some material on conformal field theory (good books are by di Francesco et al. and Ketov). Kaku goes very quickly through the more fundamental subjects before going into more difficult matter, such as string field theory, phenomenology and M-theory.
The book progresses fast beyond what might be known from basic graduate courses on superstring theory, but does not become too specific or detailed. It serves as a bridge to more advanced literature by providing somewhat more sophisticated knowledge than the average textbook (such as Polchinski).
The book is not completely self-contained, but a list of references is given at the end of each chapter, so one can find its way through the bits and pieces that are necessary to understand before proceeding.
So, in order to understand it, you need to read other books (e.g. first Zwiebach and then Polchinski or Green, Schwarz & Witten for more advanced topics and superstring theory). But in order to understand the literature, this book can be of assistance.
Strings, Conformal Fields and M-Theory.......2000-03-29
A pedagogical, single volume, introduction to String Theory and M-theory which includes recent developments in the fields. Kaku makes it a point to present the important ideas in the beginning of each chapter and summarize them in the end, at times being overly repetitive. The organization is clear and self-consistent -- a combination of a historical and a well-conceived hierarchical approach. While more readable than Polchinski and more up-to-date compared to Green, Shwartz and Witten, Kaku's book seems to lack the elegance and clout of these standard texts. Includes useful appendix and index.
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Conformal Field Theory and Topology
Toshitaki Kohno
Manufacturer: American Mathematical Society
ProductGroup: Book
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ASIN: 082182130X |
Book Description
Geometry and physics have been developed with a strong influence on each other. One of the most remarkable interactions between geometry and physics since 1980 has been an application of quantum field theory to topology and differential geometry. This book focuses on a relationship between two-dimensional quantum field theory and three-dimensional topology which has been studied intensively since the discovery of the Jones polynomial in the middle of the 1980s and Witten's invariant for 3-manifolds derived from Chern-Simons gauge theory. An essential difficulty in quantum field theory comes from infinite-dimensional freedom of a system. Techniques dealing with such infinite-dimensional objects developed in the framework of quantum field theory have been influential in geometry as well. This book gives an accessible treatment for a rigorous construction of topological invariants originally defined as partition functions of fields on manifolds.
The book is organized as follows: The Introduction starts from classical mechanics and explains basic background materials in quantum field theory and geometry. Chapter 1 presents conformal field theory based on the geometry of loop groups. Chapter 2 deals with the holonomy of conformal field theory. Chapter 3 treats Chern-Simons perturbation theory. The final chapter discusses topological invariants for 3-manifolds derived from Chern-Simons perturbation theory.
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Conformal Invariance and Critical Phenomena (Theoretical and Mathematical Physics)
Malte Henkel
Manufacturer: Springer
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Quantum Field Theory
ASIN: 354065321X |
Book Description
This book provides an introduction to conformal field theory and a review of its applications to critical phenomena in condensed-matter systems. After reviewing simple phase transitions and explaining the foundations of conformal invariance and the algebraic methods required, it proceeds to the explicit calculation of four-point correlators. Numerical methods for matrix diagonalization are described as well as finite-size scaling techniques and their conformal extensions. Many exercises are included. Applications treat the Ising, Potts, chiral Potts, Yang-Lee, percolation and XY models, the XXZ chain, linear polymers, tricritical points, conformal turbulence, surface criticality and profiles, defect lines and aperiodically modulated systems, persistent currents and dynamical scaling. The vicinity of the critical point is studied culminating in the exact solution of the two-dimensional Ising model at the critical temperature in a magnetic field. Relevant experimental results are reviewed.
Book Description
The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has recently become more prominent.
More than ten years after a first meeting in 1989 between number theorists and physicists at the Centre de Physique des Houches, a second 2-week event focused on the broader interface of number theory, geometry, and physics.
This book is the result of that exciting meeting, and collects, in 2 volumes, extended versions of the lecture courses, followed by shorter texts on special topics, of eminent mathematicians and physicists.
The present volume has three parts: Conformal Field Theories, Discrete Groups, Renomalization.
The companion volume is subtitled: On Random Matrices, Zeta Functions and Dynamical Systems (Springer, 3-540-23189-7).
Book Description
The conformal group is the invariance group of geometry (which is not understood), the largest one. Physical applications are implied, as discussed, including reasons for interactions. The group structure as well as those of related groups are analyzed. An inhomogeneous group is a subgroup of a homogeneous one because of nonlinearities of the realization. Conservation of baryons (protons can't decay) is explained and proven. Reasons for various realizations, so matrix elements, of the Lorentz group given. The clearly relevant mass level formula is compared with experimental values. Questions, implications and possibilities, including for differential equations, are raised.
Customer Reviews:
Awkward..........2007-06-15
First published in 2001 and now republished, this book is completely different from what you would expect from a "normal" textbook on mathematical physics. It has more text than formulae and the text is more or less a soup of self-citations and filled with personal scientific innuendo. The author, for instance, does not believe in the vacuum being "filled" with virtual particles, notwithstanding the experimental evidence for it, such as the Casimir effect. He calles people who do "believe" it (as if it were religion) "fools". He does not provide alternatives, but merely states his disapproval.
The text does NOT cover quantum field theory (just some (nearly trivial) basics on the Fock space at the end of the book, which can be found in any more advanced text on quantum mechanics), the conformal group is discussed neatly but not completely satisfactorily, and conformal field theory is treated very poorly (if at all!). Ronald Mirman hammers on "physics respecting its geometry", but does not provide much mathematical background for it.
Furthermore, the author is an independent researcher, which is underlined by the fact, that he does not know what belongs to a modern education in physics and what does not. He, for example, writes that the value of group theory is underappriciated in theoretical physics, which is absolutely nonsense: mathematical physics, especially particle physics, is soaked to the bone with the representation theory of Lie algebras (and in fact would not exist fully without it, to be frank).
The first chapter contains the relevance of the conformal group, in which the author does not state its application in statistical physics and string theory (which - in an online article - he thinks is useless and wrong). In this book, he talks about scale invariance of complete systems (and the role of dilations) and the relation between accelerated observers and special conformal transformations, which is interesting but not backed up mathematically much. In the second chapter, the Möbius group is treated on a basic level - the transformation of special curves (intersections of planes and conical surfaces) under the PSL(2,C) group. A bit on the Clifford algebra is given as well, but not much (and it is completely useless in the text apart from mentioning that there are fermions and bosons obeying different algebras). The conformal group, its subgroups and "similar" groups (compact and noncompact versions of so(n,m) and their covers su(n,m)) are given, but this is hardly a plus, since it is either so easy that any undergraduate could do the calculations or it is not relevant. The final chapter is about conformal field theory, but not in the usual sense (see books by e.g. Di Francesco e.a., Ketov, Kaku, Hankel, etc. for that). Mirman tries to explain what fields are and why they are useful, and what conformal transformations might be used for, but does not do much with it. Then, there are two appendices, which are not interesting either (representations of the Lorentz group & what masses of particles "tell" us - sounds more like a crystal ball to me than science!).
Besides, he says that (a large part of) mathematical literature "tries to hide [its] worthlessness under a pile of esoteric, but meaningless, language", which is more a self-description than a specification of mathematics.
The printing inside the book is okay, except that occasionally he inserts a Maple code into the text, which does not help anything and destroys the typesetting. The cover looks much better on the picture of amazon. In reality, it is a scan of the original 2001 cover, which has then been streched for the new one (at least it looks like that has been done) and one can see individual pixels.
The price is okay, although for 15$ you can get much better pieces on mathematics and physics from Dover Publications! Or invest a bit more for QFT by Itzykson & Zuber (Dover) and a CFT book by one of the authors given above.
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Quantum Non-linear Sigma-Models: From Quantum Field Theory to Supersymmetry, Conformal Field Theory, Black Holes and Strings (Theoretical and Mathematical Physics)
Sergei V. Ketov
Manufacturer: Springer
ProductGroup: Book
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ASIN: 3540674616 |
Book Description
The book is considered a systematic presentation of the modern quantum field theory of non-linear sigma-models. The contents is based on original papers. Geometrical properties and renormalization of a generic non-linear sigma-model are considered in detail, and illustrated by explicit multi-loop calculations in perturbation theory. Some non-perturbative results are derived for the conformally invariant non-linear sigma-model. Supersymmetric extensions are given for most contructions, with emphasis on their relation to complex geometry. Applications of non-linear sigma-models in conformal theory, gauge theory, string theory, and general relativity are given. The book addresses graduate sutdents and researchers in physics and mathematics.
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Conformal Field Theory
Sergei V. Ketov
Manufacturer: World Scientific Publishing Company
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Conformal Field Theory (Graduate Texts in Contemporary Physics)
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Geometry, Topology and Physics, Second Edition (Graduate Student Series in Physics)
ASIN: 9810216084 |
Book Description
Conformal field theory is an elegant and powerful theory in the field of high energy physics and statistics. In fact, it can be said to be one of the greatest achievements in the development of this field. Presented in two dimensions, this book is designed for students who already have a basic knowledge of quantum mechanics, field theory and general relativity. The main idea used throughout the book is that conformal symmetry causes both classical and quantum integrability. Instead of concentrating on the numerous applications of the theory, the author puts forward a discussion of the general methods of conformal field theory as a physical theory. Hence the book provides in a self-contained way the necessary knowledge and "conformal" intuition which underline the various applications of conformal field theory. It is aimed to assist students and professionals in the study of the theory from its first principles and in applying the methods in their own research. The first of its kind, this book promises to give a detailed and comprehensive insight into the workings of conformal field theory.
Customer Reviews:
a reference on CFT.......2006-10-27
Ketov's CFT is a very concise review of CFT and its applications to string theory and statistical mechanics. It is written well, although some effort has to be put into it to grasp all topics; more effort than with the book by di Francesco et al.. The book is nearly self-contained and might serve as a reference on CFT with some interesting examples. Each chapter provides some problems (mainly within the text) that are generally intended to do the steps between derivations. It is comparable to di Francesco's book, but on some topics they complement each other, where di Francesco presents the subjects slightly more detailed. Ketov's presentation is somewhat more mathematically oriented than di Francesco's. All in all, a very useful book on CFT for graduates.
Book Description
This is an introduction to the theory of affine Lie algebras and to the theory of quantum groups. It is unique in discussing these two subjects in a unified manner, which is made possible by discussing their respective applications in conformal field theory. The description of affine algebras covers the classification problem, the connection with loop algebras, and representation theory including modular properties. The necessary background from the theory of semisimple Lie algebras is also provided. The discussion of quantum groups concentrates on deformed enveloping algebras and their representation theory, but other aspects such as R-matrices and matrix quantum groups are also dealt with.
Books:
- Conformal Field Theory (Graduate Texts in Contemporary Physics)
- Cosmic Rays and Particle Physics
- Data Analysis: A Bayesian Tutorial
- Differential Equations, Dynamical Systems, and an Introduction to Chaos (Pure and Applied Mathematics (Academic Press), 60.)
- Einstein: His Life and Universe
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