Non-perturbative methods in two-dimensional quantum field theory.
type: Item
instance of: scholarly article
zbMATH Open document ID: 0983.81037
author: E. Abdalla
author: Maria Cristina B. Abdalla
author: K. D. Rothe
publication date: 2001-05-07T00:00:00Z
Mathematics Subject Classification ID: 81Txx
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 81-02
Mathematics Subject Classification ID: 81T16
Mathematics Subject Classification ID: 81T10
Mathematics Subject Classification ID: 81T30
Mathematics Subject Classification ID: 81V05
Mathematics Subject Classification ID: 81V10
zbMATH DE Number: 1595917
zbMATH Keywords: Thirring model
zbMATH Keywords: Gross-Neveu model
zbMATH Keywords: sine-Gordon theory
zbMATH Keywords: string theory
zbMATH Keywords: critical phenomena
zbMATH Keywords: condensed matter physics
zbMATH Keywords: nonlinear Sigma model
zbMATH Keywords: Wess-Zumino-Witten theory
zbMATH Keywords: QED
zbMATH Keywords: QCD
zbMATH Keywords: chiral gauge theories
zbMATH Keywords: conformal field theory
zbMATH Keywords: gravity
zbMATH Keywords: AdS/CFT correspondence
MaRDI profile type: Publication
title: Non-perturbative methods in two-dimensional quantum field theory.
review text: This is an extended version of a textbook, first published in 1991, on two-dimensional field theory, one of the most active areas of theoretical research between 1980 and 1995. Later on, this theory has found applications in string theory, critical phenomena in statistical physics, and general condensed matter physics. The emphasis lies on operator and functional methods rather than on perturbation expansion and numerical analysis. Since most of the properties and techniques used in this exposition are specific to two-dimensional space-time, they cast only little light on the complexity of quantum field theory in four dimensions.NEWLINENEWLINENEWLINEThe new edition is similar in scope as and therefore compares to the book published by \textit{P. Di Francesco, P. Mathieu} and \textit{D. Sénéchal} [Conformal field theory, Graduate Texts in Contemporary Physics. (1997; Zbl 0869.53052)]. Though by and large the book by Abdalla et al. covers more material, it leaves out sections on affine Lie algebras and their use in the present context. On the positive side, there are carefully written chapters on the Thirring, Gross-Neveu, and nonlinear Sigma models, as well as the sine-Gordon and Wess-Zumino-Witten theory. A large portion of the book is devoted to QED, QCD, and chiral gauge theories in two dimensions, followed by three completely rewritten and enlarged chapters on conformal field theory (CFT). The last chapter is devoted to the application of CFT to two-dimensional gravity.NEWLINENEWLINENEWLINEAs stated in the preface, the book is intended for Ph.D. students as well as for post-doctoral researchers. In particular, the last three chapters might be of interest to those who work in string theory, in view of the recently discovered AdS/CFT correspondence.
reviewed by: Gert Roepstorff
description: scientific article