Integrable Hierarchies and Modern Physical Theories / Edition 1 available in Hardcover
- Pub. Date:
- Springer Netherlands
A self-contained collection of reviews, reports and survey articles de scribing the background to and recent developments in integral systems and their applications in modern theoretical physics. Some articles d iscuss the connection of integrable models to Seiberg-Witten theory an d its generalization to many gauge models possessing hidden integrabil ity on a moduli space. New ideas are also presented on higher dimensio nal integrable systems and skyrmions. Other topics include two dimensi onal sigma and WZW models; affine and boundary integrable Toda field t heories and related perturbed conformal quantum field theories; boroni c and supersymmetric, discrete and differential KP and Toda-type hiera rchies, their various symmetry reductions, boronic and fermionic, isos pectral and non-isospectral, local and non-local flows; trigonometric Calogero-Moser systems; conjugate, orthogonal and Egorov nets. A uniqu e insight into integrable models that will interest serious practition ers, young researchers and graduate students starting their careers in the area.
Table of Contents
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.