Quantum Groups in Two-Dimensional Physics

ISBN-13: 9780521460651 / Angielski / Twarda / 1996 / 476 str.

Cesar Gomez; German Sierra; Marti Ruiz-Altaba

Opis

This 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 authors then introduce the basic ideas of integrable systems, giving particular emphasis to vertex and face models. They give special attention to the underlying mathematical tools, including braid groups, knot invariants, and towers of algebras. The authors then go on to give a detailed introduction to quantum groups before addressing 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 and will be appropriate for researchers and graduate students in theoretical physics and mathematics.

Recenzje

"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

Spis treści

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.