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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.
List of contents
From Integrable Models to Conformal Field Theories via Quantum Groups.- A brief History of hidden Quantum Symmetries in Conformal Field Theories.- q-Deformation of Semisimple and Non-semisimple Lie Algebras.- Quantum Algebras and Quantum Groups in q-special Function Theory.- Lectures in Topological Quantum Field Theory.- Canonical Quantun Gravity and the problem of time.- Higher Symmetries in Lower-dimensional Models.- Three Lectures on Supersymmetry and Extended Objects.- The Geometric Phase in Quantum Physics.- Quantum Mechanics on Phase Space.- Lie groups and solutions of nonlinear partial differential equations.
