Conformal Field Theory (Graduate Texts in Contemporary Physics)

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. TOC 1. Introduction 2. Quantum Field Theory 2.1 Quantum Fields 2.1.1. The Free Boson 2.1.2 The Free Fermion 2.2 Path Integrals 2.2.1 System with One Degree of Freedom 2.2.2 Path Integration for Quantum Fields 2.3 Correlation Functions 2.3.1 System with One Degree of Freedom 2.3.2 The Euclidian Formalism 2.3.3 The Generating Functional 2.3.4 Example: The Free Boson 2.3.5 Wick's Theorem 2.4 Symmetries and Conservation Laws 2.4.1 Continuous Symmetry Transformations 2.4.2 Infinitesimal Transformations and Noether's Theorem 2.4.3 Transformation of the Correlation Functions 2.4.4 Ward Identities 2.5 Energy-Momentum Tensor 2.5.1 The Belinfante Tensor 2.5.2 Alternate Definition of the Energy-Momentum Tensor 2.A Gaussian Integrals 2.B Grassmann Variables 2.C Tetrads Exercises