Discrete Integrable Geometry and Physics
by Bobenko, Alexander I.; Seiler, RuediFormat: Hardcover
Pub. Date: 1999-08-26
Publisher(s): Oxford University Press
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Summary
Recent interactions between the fields of geometry, classical and quantum dynamical systems, and the visualization of geometric objects have led to the observation that most concepts of surface theory and of the theory of integrable systems have natural discrete analogues. For these analogues the corresponding difference equations are often integrable, which has in turn led to important results in such areas as condensed matter physics and quantum field theory. This book combines the efforts of a distinguished team of authors from various fields in mathematics and physics to provide an accessible overview of the subject. The book begins with the mathematical concepts of discrete geometry and discrete integrable systems, which are interesting on their own, and then proceeds to develop the many connections with classical and quantum dynamics.
Table of Contents
| List of contributors | |
| Introduction | |
| Geometry | |
| Discretization of Surfaces and Integrable Systems | |
| A Discrete Version of the Darboux Transform for Isothermic Surfaces | |
| Discrete Amsler Surfaces and a Discrete Painleve III Equation | |
| Discrete cmc Surfaces and Discrete Holomorphic Maps | |
| Discrete Indefinite Affine Spheres | |
| Geometry of Discrete Curves and Lattices and Integrable Difference Equations | |
| Classical Systems | |
| R-matrices and Integrable Discretizations | |
| Discrete Painleve Equations and Symmetry Reduction on the Lattice | |
| Lagrangian Description of Doubly Discrete Sine-Gordon Type Models | |
| Quantum Systems | |
| Spectra of Quantum Integrals | |
| Algebraic Quantization of Integrable Models in Discrete Space-Time | |
| Affine Toda Field Theory as a Three-dimensional Integrable System | |
| Quantum Hyperbolic Invariants of Knots | |
| Charge Transport in the Discretized Landau Model | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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