Quantum Groups in Two-Dimensional Physics

A 1996 introduction to integrability and conformal field theory in two dimensions using quantum groups.

Cisar Gómez (Author), Martm Ruiz-Altaba (Author), German Sierra (Author)

9780521460651, Cambridge University Press

Hardback, published 18 April 1996

476 pages, 125 b/w illus. 20 tables 150 exercises
24.4 x 17 x 2.7 cm, 0.95 kg

"The book is written in a simple and lucid manner, that allows one to suggest it for an audience with no previous acquaintance with the subject. This book will be of use to graduate students and researchers in theoretical physics and applied mathematics interested in integrable systems, string theory and conformal field theory." Audrey V. Tsiganov, Mathematical Reviews

This 1996 book is an introduction to integrability and conformal field theory in two dimensions using quantum groups. The book begins with a brief introduction to S-matrices, spin chains and vertex models as a prelude to the study of Yang–Baxter algebras and the Bethe ansatz. The basic ideas of integrable systems are then introduced, giving particular emphasis to vertex and face models. Special attention is given to explaining the underlying mathematical tools, including braid groups, knot invariants and towers of algebra. The book then goes on to give a detailed introduction to quantum groups as a prelude to chapters on integrable models, two-dimensional conformal field theories and superconformal field theories. The book contains many diagrams and exercises to illustrate key points in the text.

Preface
1. S-matrices, spin chains and vertex models
2. The Yang–Baxter equation - a first look
3. Bethe ansatz - some examples
4. The eight-vertex model
5. Face models
6. Quantum groups - mathematical review
7. Integrable models at roots of unit
8. Two-dimensional conformal field theories
9. Duality in conformal field theories
10. Coulomb gas representation
11. Quantum groups in conformal field theory.

Subject Areas: Physics [PH]