Download or read book Conformal Field Theory written by Philippe Francesco and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 908 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Conformal Field Theory written by Ralph Blumenhagen and published by Springer. This book was released on 2009-07-11 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on class-tested notes, this text offers an introduction to Conformal Field Theory with a special emphasis on computational techniques of relevance for String Theory. It introduces Conformal Field Theory at a basic level, Kac-Moody algebras, one-loop partition functions, Superconformal Field Theories, Gepner Models and Boundary Conformal Field Theory. Eventually, the concept of orientifold constructions is explained in detail for the example of the bosonic string. In providing many detailed CFT calculations, this book is ideal for students and scientists intending to become acquainted with CFT techniques relevant for string theory but also for students and non-specialists from related fields.
Download or read book A Mathematical Introduction to Conformal Field Theory written by Martin Schottenloher and published by Springer Science & Business Media. This book was released on 2008-09-15 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part I gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. The conformal groups are determined and the appearence of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. Part II surveys more advanced topics of conformal field theory such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface.
Download or read book Conformal Field Theory and Topology written by Toshitake Kohno and published by American Mathematical Soc.. This book was released on 2002 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 invariantfor 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 geometryas 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 treatsChern-Simons perturbation theory. The final chapter discusses topological invariants for 3-manifolds derived from Chern-Simons perturbation theory.
Download or read book EPFL Lectures on Conformal Field Theory in D 3 Dimensions written by Slava Rychkov and published by Springer. This book was released on 2016-09-30 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer develops Conformal Field Theory (CFT) from scratch, whereby CFT is viewed as any conformally-invariant theory that describes a fixed point of a renormalization group flow in quantum field theory. The book is divided into four lectures: Lecture 1 addresses the physical foundations of conformal invariance, while Lecture 2 examines the constraints imposed by conformal symmetry on the correlation functions of local operators, presented using the so-called projective null cone – a procedure also known as the embedding formalism. In turn, Lecture 3 focuses on the radial quantization and the operator product expansion, while Lecture 4 offers a very brief introduction to the conformal bootstrap. Derived from course-based notes, these lectures are intended as a first point of entry to this topic for Master and PhD students alike.
Download or read book Conformal Field Theory written by Sergei V Ketov and published by World Scientific. This book was released on 1995-02-28 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Conformal Field Theory written by Yavuz Nutku and published by CRC Press. This book was released on 2018-03-14 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an understanding of conformal field theory and its importance to both statistical mechanics and string theory. It introduces the Wess-Zumino-Novokov-Witten (WZNW) models and their current algebras, the affine Kac-Moody algebras.
Download or read book Conformal Quantum Field Theory in D dimensions written by E.S. Fradkin and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our prime concern in this book is to discuss some most interesting prosppcts that have occurred recently in conformally invariant quantum field theory in a D-diuwnsional space. One of the most promising trends is constructing an pxact solution for a cprtain class of models. This task seems to be quite feasible in the light of recent resllits. The situation here is to some extent similar to what was going on in the past ypars with the two-dimensional quantum field theory. Our investigation of conformal Ward identities in a D-dimensional space, carried out as far hack as the late H. J7Gs, showed that in the D-dimensional quantum field theory, irrespective of the type of interartion, there exists a special set of states of the field with the following property: if we rpqllire that one of these states should vanish, this determines an exact solution of 3. certain field model. These states are analogous to null-vectors which determine the minimal models in the two-dimensional field theory. On the other hand, the recent resparches supplied us with a number of indications on the existencp of an intinite-parampter algebra analogous to the Virasoro algebra in spaces of higher dimensions D 2: :~. It has also been shown that this algebra admits an operator rentral expansion. It seems to us that the above-mentioned models are field theoretical realizations of the representations of these new symmetries for D 2: ;3.
Download or read book Quantum Field Theory Conformal Group Theory Conformal Field Theory written by R. Mirman and published by iUniverse. This book was released on 2005-02 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Non Perturbative Field Theory written by Yitzhak Frishman and published by Cambridge University Press. This book was released on 2010-04-08 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a new perspective on quantum field theory, this book is useful for graduate students and researchers within and outside the field. It describes non-perturbative methods, and explores two-dimensional and four-dimensional gauge dynamics using those methods. Applications are thoroughly described.
Download or read book Boundary Conformal Field Theory and the Worldsheet Approach to D Branes written by Andreas Recknagel and published by Cambridge University Press. This book was released on 2013-11-28 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary conformal field theory is concerned with a class of two-dimensional quantum field theories which display a rich mathematical structure and have many applications ranging from string theory to condensed matter physics. In particular, the framework allows discussion of strings and branes directly at the quantum level. Written by internationally renowned experts, this comprehensive introduction to boundary conformal field theory reaches from theoretical foundations to recent developments, with an emphasis on the algebraic treatment of string backgrounds. Topics covered include basic concepts in conformal field theory with and without boundaries, the mathematical description of strings and D-branes, and the geometry of strongly curved spacetime. The book offers insights into string geometry that go beyond classical notions. Describing the theory from basic concepts, and providing numerous worked examples from conformal field theory and string theory, this reference is of interest to graduate students and researchers in physics and mathematics.
Download or read book Physics and Mathematics of Strings written by Lars Brink and published by World Scientific. This book was released on 1990 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vadim Knizhnik was one of the most promising theoretical physicists in the world. Unfortunately, he passed away at the very young age of 25 years. This memorial volume is to honor his contributions in Theoretical Physics. This is perhaps one of the most important collections of articles on the theoretical developments in String Theory, Conformal Field Theory and related topics. It consists of contributions from world-renowned physicists who have met Vadim Knizhnik personally and whom the late Knizhnik really respected. The contributions are systematic and pedagogical in format.
Download or read book Differential Geometrical Methods in Theoretical Physics written by K. Bleuler and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Research Workshop and the 16th International Conference, Como, Italy, August 24-29, 1987
Download or read book Conformal Field Theory with Gauge Symmetry written by Kenji Ueno and published by American Mathematical Soc.. This book was released on 2008 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic approach to conformal field theory with gauge symmetry from the point of view of complex algebraic geometry. After presenting the basic facts of the theory of compact Riemann surfaces and the representation theory of affine Lie algebras in Chapters 1 and 2, conformal blocks for pointed Riemann surfaces with coordinates are constructed in Chapter 3. In Chapter 4 the sheaf of conformal blocks associated to a family of pointed Riemann surfaces withcoordinates is constructed, and in Chapter 5 it is shown that this sheaf supports a projective flat connection-one of the most important facts of conformal field theory. Chapter 6 is devoted to the study of the detailed structure of the conformal field theory over $\mathbb{P}1$.Recently it was shown that modular functors can be constructed from conformal field theory, giving an interesting relationship between algebraic geometry and topological quantum field theory. This book provides a timely introduction to an intensively studied topic of conformal field theory with gauge symmetry by a leading algebraic geometer, and includes all the necessary techniques and results that are used to construct the modular functor.
Download or read book Strings Conformal Fields and M Theory written by Michio Kaku and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Throughout, the author conveys the vitality of the current research and places readers at its forefront. Several chapters reviewing the fundamentals of string theory, making the presentation of the material self-contained while keeping overlap with the earlier book to a minimum.
Download or read book Conformal Invariance And Applications To Statistical Mechanics written by C Itzykson and published by World Scientific. This book was released on 1998-09-29 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains Introductory Notes and major reprints on conformal field theory and its applications to 2-dimensional statistical mechanics of critical phenomena. The subject relates to many different areas in contemporary physics and mathematics, including string theory, integrable systems, representations of infinite Lie algebras and automorphic functions.
Download or read book Conformal Field Theory and Solvable Lattice Models written by M Jimbo and published by Elsevier. This book was released on 2012-12-02 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Studies in Pure Mathematics, 16: Conformal Field Theory and Solvable Lattice Models contains nine papers based on the symposium "Conformal field theory and solvable lattice models" held at RIMS, Kyoto, May 1986. These papers cover the following active areas in mathematical physics: conformal field theory, solvable lattice models, affine and Virasoro algebra, and KP equations. The volume begins with an analysis of 1 and 2 point correlation functions of the Gibbs measure of random matrices. This is followed by separate chapters on solvable solid-on-solid (SOS) models; lectures on conformal field theory; the construction of Fermion variables for the 3D Ising Model; and vertex operator construction of null fields (singular vertex operators) based on the oscillator representation of conformal and superconformal algebras with central charge extention. Subsequent chapters deal with Hecke algebra representations of braid groups and classical Yang-Baxter equations; the relationship between the conformal field theories and the soliton equations (KdV, MKdV and Sine-Gordon, etc.) at both quantum and classical levels; and a supersymmetric extension of the Kadomtsev-Petviashvili hierarchy.
