Integrable Systems, Quantum Groups, and Quantum Field Theories

1. Front Matter

   Pages i-xi

   PDF

2. From Integrable Models to Conformal Field Theory Via Quantum Groups

   • L. D. Faddeev

   Pages 1-24

3. A Brief History of Hidden Quantum Symmetries in Conformal Field Theories

   • César Gómez, Germán Sierra

   Pages 25-43

4. q-Deformation of Semisimple and Non-Semisimple Lie Algebras

   • Henri Ruegg

   Pages 45-81

5. Quantum Algebras and Quantum Groups in q-Special Function Theory

   • Roberto Floreanini, Luc Vinet

   Pages 83-94

6. Lectures on Topological Quantum Field Theory

   • Daniel S. Freed

   Pages 95-156

7. Canonical Quantum Gravity and the Problem of Time

   • C. J. Isham

   Pages 157-287

8. Higher Symmetries in Lower-Dimensional Models

   • R. Jackiw

   Pages 289-316

9. Three Lectures on Supersymmetry and Extended Objects

   • P. K. Townsend

   Pages 317-345

10. The Geometric Phase in Quantum Physics

    • A. Bohm

    Pages 347-415

11. Quantum Mechanics on Phase Space

    • M. Gadella

    Pages 417-428

12. Lie Groups and Solutions of Nonlinear Partial Differential Equations

    • P. Winternitz

    Pages 429-495

13. Back Matter

    Pages 497-502

    PDF

In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.

• Theoretical physics
• algebra
• conformal field theory
• mathematical physics
• mathematics
• mechanics
• partial differential equation
• quantum field theory
• quantum mechanics
• quantum physics
• partial differential equations

• Departamento de Física Teórica, Universidad Complutense de Madrid, Madrid, Spain

  L. A. Ibort, M. A. Rodríguez

Policies and ethics