Conformal Field Theory

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Conformal Field Theory

Philippe Francesco,Pierre Mathieu,David Senechal
Conformal Field Theory Book PDF

Author : Philippe Francesco,Pierre Mathieu,David Senechal
Publisher : Springer Science & Business Media
Page : 908 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461222569

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Conformal Field Theory by Philippe Francesco,Pierre Mathieu,David Senechal Pdf

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.

Introduction to Conformal Field Theory

Ralph Blumenhagen,Erik Plauschinn
Introduction to Conformal Field Theory Book PDF

Author : Ralph Blumenhagen,Erik Plauschinn
Publisher : Springer
Page : 265 pages
File Size : 45,9 Mb
Release : 2009-07-11
Category : Science
ISBN : 9783642004506

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Introduction to Conformal Field Theory by Ralph Blumenhagen,Erik Plauschinn Pdf

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.

Conformal Field Theory and Topology

Toshitake Kohno
Conformal Field Theory and Topology Book PDF

Author : Toshitake Kohno
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 49,5 Mb
Release : 2002
Category : Mathematics
ISBN : 082182130X

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Conformal Field Theory and Topology by Toshitake Kohno Pdf

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.

A Mathematical Introduction to Conformal Field Theory

Martin Schottenloher
A Mathematical Introduction to Conformal Field Theory Book PDF

Author : Martin Schottenloher
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 46,6 Mb
Release : 2008-09-15
Category : Science
ISBN : 9783540706908

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A Mathematical Introduction to Conformal Field Theory by Martin Schottenloher Pdf

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.

EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions

Slava Rychkov
EPFL Lectures on Conformal Field Theory in D 3 Dimensions Book PDF

Author : Slava Rychkov
Publisher : Springer
Page : 72 pages
File Size : 54,5 Mb
Release : 2016-09-30
Category : Science
ISBN : 9783319436265

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EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions by Slava Rychkov Pdf

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.

Conformal Field Theory

Sergei V Ketov
Conformal Field Theory Book PDF

Author : Sergei V Ketov
Publisher : World Scientific
Page : 502 pages
File Size : 43,6 Mb
Release : 1995-02-28
Category : Science
ISBN : 9789814502528

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Conformal Field Theory by Sergei V Ketov Pdf

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.

Conformal Field Theory

Yavuz Nutku,Cihan Saclioglu,Teoman Turgut
Conformal Field Theory Book PDF

Author : Yavuz Nutku,Cihan Saclioglu,Teoman Turgut
Publisher : CRC Press
Page : 413 pages
File Size : 49,6 Mb
Release : 2018-03-14
Category : Science
ISBN : 9780429971426

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Conformal Field Theory by Yavuz Nutku,Cihan Saclioglu,Teoman Turgut Pdf

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.

Non-Perturbative Field Theory

Yitzhak Frishman,Jacob Sonnenschein
Non Perturbative Field Theory Book PDF

Author : Yitzhak Frishman,Jacob Sonnenschein
Publisher : Cambridge University Press
Page : 455 pages
File Size : 48,7 Mb
Release : 2010-04-08
Category : Science
ISBN : 9781139486484

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Non-Perturbative Field Theory by Yitzhak Frishman,Jacob Sonnenschein Pdf

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.

Conformal Quantum Field Theory in D-dimensions

E.S. Fradkin,Mark Ya. Palchik
Conformal Quantum Field Theory in D dimensions Book PDF

Author : E.S. Fradkin,Mark Ya. Palchik
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 49,6 Mb
Release : 2013-03-14
Category : Science
ISBN : 9789401587570

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Conformal Quantum Field Theory in D-dimensions by E.S. Fradkin,Mark Ya. Palchik Pdf

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.

Conformal Field Theory with Gauge Symmetry

Kenji Ueno
Conformal Field Theory with Gauge Symmetry Book PDF

Author : Kenji Ueno
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 52,9 Mb
Release : 2008
Category : Conformal invariants
ISBN : 9780821840887

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Conformal Field Theory with Gauge Symmetry by Kenji Ueno Pdf

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.

Quantum Field Theory Conformal Group Theory Conformal Field Theory

R. Mirman
Quantum Field Theory Conformal Group Theory Conformal Field Theory Book PDF

Author : R. Mirman
Publisher : iUniverse
Page : 313 pages
File Size : 42,8 Mb
Release : 2005-02
Category : Science
ISBN : 9780595336920

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Quantum Field Theory Conformal Group Theory Conformal Field Theory by R. Mirman Pdf

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.

Boundary Conformal Field Theory and the Worldsheet Approach to D-Branes

Andreas Recknagel,Volker Schomerus
Boundary Conformal Field Theory and the Worldsheet Approach to D Branes Book PDF

Author : Andreas Recknagel,Volker Schomerus
Publisher : Cambridge University Press
Page : 349 pages
File Size : 44,9 Mb
Release : 2013-11-28
Category : Science
ISBN : 9781107511804

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Boundary Conformal Field Theory and the Worldsheet Approach to D-Branes by Andreas Recknagel,Volker Schomerus Pdf

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.

Conformal Field Theory and Solvable Lattice Models

M Jimbo
Conformal Field Theory and Solvable Lattice Models Book PDF

Author : M Jimbo
Publisher : Elsevier
Page : 438 pages
File Size : 47,5 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323150354

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Conformal Field Theory and Solvable Lattice Models by M Jimbo Pdf

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.

Quantum Non-linear Sigma-Models

Sergei V. Ketov
Quantum Non linear Sigma Models Book PDF

Author : Sergei V. Ketov
Publisher : Springer Science & Business Media
Page : 429 pages
File Size : 54,5 Mb
Release : 2013-03-09
Category : Science
ISBN : 9783662041925

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Quantum Non-linear Sigma-Models by Sergei V. Ketov Pdf

This is the first comprehensive presentation of the quantum non-linear sigma-models. The original papers consider in detail geometrical properties and renormalization of a generic non-linear sigma-model, illustrated by explicit multi-loop calculations in perturbation theory.

Quantum Field Theory: A Tourist Guide for Mathematicians

Gerald B. Folland
Quantum Field Theory A Tourist Guide for Mathematicians Book PDF

Author : Gerald B. Folland
Publisher : American Mathematical Soc.
Page : 325 pages
File Size : 41,5 Mb
Release : 2021-02-03
Category : Education
ISBN : 9781470464837

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Quantum Field Theory: A Tourist Guide for Mathematicians by Gerald B. Folland Pdf

Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam–Weinberg model of electromagnetic and weak interactions.