Integrable Hierarchies and Modern Physical Theories

ISBN-13: 9780792369639 / Angielski / Miękka / 2001 / 435 str.

Henrik Aratyn; Alexander S. Sorin

Opis

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.

Spis treści

Preface. List of Contributors. Seiberg-Witten Toda Chains and N=1 SQCD; A. Marshakov. Integrable Hierarchies in Donaldson-Witten and Seiberg-Witten Theories; J.D. Edelstein, M. Gomez-Reino. Integrable Many-Body Systems and Gauge Theories; A. Gorsky, A. Mironov. From PCM to KdV and Back; J.M. Evans. Reflection Amplitudes in Conformal Field Theory and Integrable Systems; V.A. Fateev. Lagrangian Approach to Integrable Systems Yields New Symplectic Structures for KdV; Y. Nutku. Skyrmions from Harmonic Maps; P.M. Sutcliffe, W.J. Zakrzewski. Symmetry Flows, Conservations Laws and Dressing Approach to the Integrable Models; H. Aratyn, et al. Trigonometric Calogero-Moser System as a Symmetry Reduction of KP Hierarchy; L.V. Bogdanov, et al. Supersymmetric Toda Lattice Hierarchies; V.G. Kadyshevsky, A.S. Sorin. Symmetries and Recursions for N = 2 Supersymmetric KdV-equation; P.H.M. Kersten. New Solvable Periodic Potentials from Supersymmetry; U. Sukhatme. Functional and Differential Equations in the Problems of Nonlinear Mathematical Physics; A.N. Leznov. Integrable Multi-Dimensional Discrete Geometry. Quadrilateral lattices, their transformations and reductions; A. Doliwa. Integrable Nets and the KP Hierarchy; M. Mañas, L. Martínez Alonso. A Survey of Star Product Geometry; C. Zachos.