Ebook: 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.

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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.
Content:
Front Matter....Pages i-x
Seiberg-Witten Toda Chains and N=1 SQCD....Pages 1-13
Integrable Hierarchies in Donaldson-Witten and Seiberg-Witten Theories....Pages 15-32
Integrable Many-Body Systems and Gauge Theories....Pages 33-176
From PCM to KDV and Back....Pages 177-178
Reflection Amplitudes in Conformal Field Theory and Integrable Systems....Pages 179-201
Lagrangian Approach to Integrable Systems Yields New Symplectic Structures for KDV....Pages 203-213
Skyrmions from Harmonic Maps....Pages 215-241
Symmetry Flows, Conservation Laws and Dressing Approach to the Integrable Models....Pages 243-275
Trigonometric Calogero-Moser System as a Symmetry Reduction of KP Hierarchy....Pages 277-287
Supersymmetric Toda Lattice Hierarchies....Pages 289-316
Symmetries and Recursions For N = 2 Supersymmetric KDV-Equation....Pages 317-327
New Solvable Periodic Potentials from Supersymmetry....Pages 329-338
Functional and Differential Equations in The Problems of Nonlinear Mathematical Physics....Pages 339-354
Integrable Multidimensional Discrete Geometry....Pages 355-389
Integrable Nets and the KP Hierarchy....Pages 391-421
A Survey of Star Product Geometry....Pages 423-435

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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.
Content:
Front Matter....Pages i-x
Seiberg-Witten Toda Chains and N=1 SQCD....Pages 1-13
Integrable Hierarchies in Donaldson-Witten and Seiberg-Witten Theories....Pages 15-32
Integrable Many-Body Systems and Gauge Theories....Pages 33-176
From PCM to KDV and Back....Pages 177-178
Reflection Amplitudes in Conformal Field Theory and Integrable Systems....Pages 179-201
Lagrangian Approach to Integrable Systems Yields New Symplectic Structures for KDV....Pages 203-213
Skyrmions from Harmonic Maps....Pages 215-241
Symmetry Flows, Conservation Laws and Dressing Approach to the Integrable Models....Pages 243-275
Trigonometric Calogero-Moser System as a Symmetry Reduction of KP Hierarchy....Pages 277-287
Supersymmetric Toda Lattice Hierarchies....Pages 289-316
Symmetries and Recursions For N = 2 Supersymmetric KDV-Equation....Pages 317-327
New Solvable Periodic Potentials from Supersymmetry....Pages 329-338
Functional and Differential Equations in The Problems of Nonlinear Mathematical Physics....Pages 339-354
Integrable Multidimensional Discrete Geometry....Pages 355-389
Integrable Nets and the KP Hierarchy....Pages 391-421
A Survey of Star Product Geometry....Pages 423-435
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