Recent interactions between the fields of geometry, classical and quantum dynamical systems, and visualization of geometric objects such as curves and surfaces have led to the observation that most concepts of surface theory and of the theory of integrable systems have natural discrete analogues. These are characterized by the property that the corresponding difference equations are integrable, and has led in turn to some important applications in areas of condensed matter physics and quantum field theory, amongst others. The book combines the efforts of a distinguished team of authors from various fields in mathematics and physics in an effort to provide an overview of the subject. The mathematical concepts of discrete geometry and discrete integrable systems are firstly presented as fundamental and valuable theories in themselves. In the following part these concepts are put into the context of classical and quantum dynamics.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Illustrationen
12 Bildtafeln, 84 Schaubilder
12 plates, 84 line figures
Maße
Höhe: 234 mm
Breite: 156 mm
Gewicht
ISBN-13
978-0-19-850160-2 (9780198501602)
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Schweitzer Klassifikation
I: GEOMETRY; 1. A. Bobenko & U. Pinkall; Discretization of Surfaces and Integrable Systems; 2. U. Hertrich-Jeromin, T. Hoffmann & U. Pinkall; A Discrete Version of the Darboux Transform for Isothermic Surfaces Darboux Transform for Isothermic Surfaces; 3. T. Hoffmann; Discrete Amsler Surfaces and a Discrete Painleve III Equation; 4. T. Hoffmann; Discrete cmc Surfaces and Discrete Holomorphic Maps; 5. A. Bobenko & W. Schief; Discrete Indefinite Affine Spheres; 6. A. Doliwa & P. M. Santini; Geometry of Discrete Curves and Lattices and Integrable Difference Equations; II: CLASSICAL SYSTEMS; 7. Y. Suris; R-matrices and Integrable Discretizations; 8. F. Nijhoff; Discrete Painleve Equations and Symmetry Reduction on the Lattice; 9. N. Kutz; Lagrangian Description of Doubly Discrete Sine-Gordon Type Models; III: QUANTUM SYSTEMS; 10. J. Kellendonk, N. Kutz & R. Seiler; Spectra of Quantum Integrals; 11. L. Faddeev & A. Volkov; Algebraic Quantization of Integrable Models in Discrete Space-Time; 12. R. Kashaev & N. Reshetikhin; Affine Toda Field Theory as a Three-Dimensional Integrable System; 13. R. Kashaev; Quantum Hyperbolic Invariants of Knots; 14. T. Richter & R. Seiler; Charge Transport in the Discretized Landau Model
