Integrable Hierarchies and Modern Physical Theories

A self-contained collection of reviews, reports and survey articles describing the background to and recent developments in integral systems and their applications in modern theoretical physics. Some articles discuss the connection of integrable models to Seiberg-Witten theory and its generalization to many gauge models possessing hidden integrability on a moduli space. New ideas are also presented on higher dimensional integrable systems and skyrmions. Other topics include two dimensional sigma and WZW models; affine and boundary integrable Toda field theories and related perturbed conformal quantum field theories; boronic and supersymmetric, discrete and differential KP and Toda-type hierarchies, their various symmetry reductions, boronic and fermionic, isospectral and non-isospectral, local and non-local flows; trigonometric Calogero-Moser systems; conjugate, orthogonal and Egorov nets.
A unique insight into integrable models that will interest serious practitioners, young researchers and graduate students starting their careers in the area.

List of contents

Seiberg-Witten Toda Chains and N=1 SQCD.- Integrable Hierarchies in Donaldson-Witten and Seiberg-Witten Theories.- Integrable Many-Body Systems and Gauge Theories.- From PCM to KdV and Back.- Reflection Amplitudes in Conformai Field Theory and Integrable Systems.- Lagrangian Approach to Integrable Systems Yields New Symplectic Structures for KdV.- Skyrmions from Harmonic Maps.- Symmetry Flows, Conservation Laws and Dressing Approach to the Integrable Models.- Trigonometric Calogero-Moser System as a Symmetry Reduction of KP Hierarchy.- Supersymmetric Toda Lattice Hierarchies.- Symmetries and Recursions for N = 2 Supersymmetric KdV-equation.- New Solvable Periodic Potentials from Supersymmetry.- Functional and Differential Equations in the Problems of Nonlinear Mathematical Physics.- Integrable Multi-Dimensional Discrete Geometry. Quadrilateral lattices, their transformations and reductions.- Integrable Nets and the KP Hierarchy.- A Survey of Star Product Geometry.

Summary

Proceedings of the NATO Advanced Research Workshop, Chicago, USA, July 22-26, 2000

Product details

• Assisted by: Henri Aratyn (Editor), Henrik Aratyn (Editor), S Sorin (Editor), S Sorin (Editor), Alexander S. Sorin (Editor)
• Publisher: Springer Netherlands
• Languages: English
• Product format: Hardback
• Released: 01.02.2011
• EAN: 9780792369622
• ISBN: 978-0-7923-6962-2
• No. of pages: 435
• Weight: 830 g
• Illustrations: X, 435 p.
• Series: NATO Science Series II Mathematics, Physics and Chemistry; Nato Science Series II: NATO Science Series II: Mathematics, Physics and Chemistry; NATO Science Series II
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Theoretical physics; Algebra, B, Chemistry and Materials Science, Applications of Mathematics, Algebraic Geometry, Theoretical, Mathematical and Computational Physics, Mathematical physics, Rings (Algebra), Non-associative Rings and Algebras, Nonassociative rings, Partial Differential Equations, Differential calculus & equations, Differential equations, Engineering mathematics, Applied mathematics