Non-perturbative methods in two-dimensional quantum field theory.
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.
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