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Quantum Field Theory Conformal Group Theory Conformal Field Theory
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Book Synopsis Quantum Field Theory Conformal Group Theory Conformal Field Theory by : R. Mirman
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.
Book Synopsis A Mathematical Introduction to Conformal Field Theory by : Martin Schottenloher
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.
Book Synopsis Conformal Field Theory by : Philippe Francesco
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.
Book Synopsis EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions by : Slava Rychkov
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 72 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.
Book Synopsis Conformal Field Theory by : Sergei V Ketov
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.
Book Synopsis Conformal Field Theory by : Yavuz Nutku
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 413 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.
Book Synopsis Introduction to Conformal Field Theory by : Ralph Blumenhagen
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 265 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.
Book Synopsis Conformal Quantum Field Theory in D-dimensions by : E.S. Fradkin
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.
Book Synopsis Conformal Field Theory for Particle Physicists by : Marc Gillioz
Download or read book Conformal Field Theory for Particle Physicists written by Marc Gillioz and published by Springer Nature. This book was released on 2023-04-13 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a set of introductory lecture notes on Conformal Field Theory (CFT). Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. The book starts with a non-perturbative formulation of quantum field theory (Wightman axioms) and then, gradually, focuses on the implications of scale and special conformal symmetry, all the way to the modern conformal bootstrap. This approach includes topics such as subtleties of conformal transformations in Minkowski space-time, the construction of Wightman functions and time-ordered correlators both in position- and momentum-space, unitarity bounds derived from the spectral representation, and the appearance of UV and IR divergences. In each chapter, the reader finds useful exercises to master the subject. This book is meant for graduate students in theoretical physics and for more advanced researchers working in high-energy physics who are not necessarily familiar with the concepts of conformal field theory. Prior knowledge of quantum field theory is needed to master the arguments.
Book Synopsis Conformal Field Theory and Topology by : Toshitake Kohno
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.
Book Synopsis Boundary Conformal Field Theory and the Worldsheet Approach to D-Branes by : Andreas Recknagel
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.
Book Synopsis Conformal Invariance And Applications To Statistical Mechanics by : C Itzykson
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 Harmonic Analysis written by V. K. Dobrev and published by Springer. This book was released on 1977-04-01 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Mathematical Introduction to Conformal Field Theory by : Martin Schottenloher
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 2008-09-26 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book gives a self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. The second part surveys some more advanced topics of conformal field theory.
Download or read book W-symmetry written by P. Bouwknegt and published by World Scientific. This book was released on 1995 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt: W-symmetry is an extension of conformal symmetry in two dimensions. Since its introduction in 1985, W-symmetry has become one of the central notions in the study of two-dimensional conformal field theory. The mathematical structures that underlie W-symmetry are so-called W-algebras, which are higher-spin extensions of the Virasoro algebra. This book contains a collection of papers on W-symmetry, covering the period from 1985 through 1993. Its main focus is the construction of W-algebras and their representation theory. A recurrent theme is the intimate connection between W-algebras and affine Lie algebras. Some of the applications, in particular W-gravity, are also covered.The significance of this reprint volume is that there are no textbooks entirely devoted to the subject.
Book Synopsis Conformal invariance in quantum field theory by : Ivan T. Todorov
Download or read book Conformal invariance in quantum field theory written by Ivan T. Todorov and published by Edizioni della Normale. This book was released on 1978-10-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is an extended and up-to-date version of two sets of lectures by the first author and it reviews more recent work. The notes aim to present a self-contained exposition of a constructive approach to conformal invariant quantum field theory. Other parts in application of the conformal group to quantum physics are only briefly mentioned. The relevant mathematical material (harmonic analysis on Euclidean conformal groups) is briefly summarized. A new exposition of physical applications is given, which includes an explicit construction of the vacuum operator product expansion for the free zero mass fields.
Book Synopsis Renormalization and Effective Field Theory by : Kevin Costello
Download or read book Renormalization and Effective Field Theory written by Kevin Costello and published by American Mathematical Soc.. This book was released on 2011 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorious difficulties of renormalization have made quantum field theory very inaccessible for mathematicians. This provides complete mathematical foundations for the theory of perturbative quantum field theory, based on Wilson's ideas of low-energy effective field theory and on the Batalin-Vilkovisky formalism.
