Ebook: Integrable Systems, Quantum Groups, and Quantum Field Theories
- Tags: Theoretical Mathematical and Computational Physics, Non-associative Rings and Algebras, Topological Groups Lie Groups, Partial Differential Equations
- Series: NATO ASI Series 409
- Year: 1993
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- 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.
Content:
Front Matter....Pages i-xi
From Integrable Models to Conformal Field Theory Via Quantum Groups....Pages 1-24
A Brief History of Hidden Quantum Symmetries in Conformal Field Theories....Pages 25-43
q-Deformation of Semisimple and Non-Semisimple Lie Algebras....Pages 45-81
Quantum Algebras and Quantum Groups in q-Special Function Theory....Pages 83-94
Lectures on Topological Quantum Field Theory....Pages 95-156
Canonical Quantum Gravity and the Problem of Time....Pages 157-287
Higher Symmetries in Lower-Dimensional Models....Pages 289-316
Three Lectures on Supersymmetry and Extended Objects....Pages 317-345
The Geometric Phase in Quantum Physics....Pages 347-415
Quantum Mechanics on Phase Space....Pages 417-428
Lie Groups and Solutions of Nonlinear Partial Differential Equations....Pages 429-495
Back Matter....Pages 497-502
Content:
Front Matter....Pages i-xi
From Integrable Models to Conformal Field Theory Via Quantum Groups....Pages 1-24
A Brief History of Hidden Quantum Symmetries in Conformal Field Theories....Pages 25-43
q-Deformation of Semisimple and Non-Semisimple Lie Algebras....Pages 45-81
Quantum Algebras and Quantum Groups in q-Special Function Theory....Pages 83-94
Lectures on Topological Quantum Field Theory....Pages 95-156
Canonical Quantum Gravity and the Problem of Time....Pages 157-287
Higher Symmetries in Lower-Dimensional Models....Pages 289-316
Three Lectures on Supersymmetry and Extended Objects....Pages 317-345
The Geometric Phase in Quantum Physics....Pages 347-415
Quantum Mechanics on Phase Space....Pages 417-428
Lie Groups and Solutions of Nonlinear Partial Differential Equations....Pages 429-495
Back Matter....Pages 497-502
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