Introduction to Classical Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Classical Integrable Systems write by Olivier Babelon. This book was released on 2003-04-17. Introduction to Classical Integrable Systems available in PDF, EPUB and Kindle. This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.
Elements of Classical and Quantum Integrable Systems
Elements of Classical and Quantum Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elements of Classical and Quantum Integrable Systems write by Gleb Arutyunov. This book was released on 2019-07-23. Elements of Classical and Quantum Integrable Systems available in PDF, EPUB and Kindle. Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.
Global Aspects of Classical Integrable Systems
Global Aspects of Classical Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Global Aspects of Classical Integrable Systems write by Richard H. Cushman. This book was released on 2015-06-01. Global Aspects of Classical Integrable Systems available in PDF, EPUB and Kindle. This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.
Quantum Integrable Systems
Quantum Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Integrable Systems write by Asesh Roy Chowdhury. This book was released on 2004-01-28. Quantum Integrable Systems available in PDF, EPUB and Kindle. The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists alike, and none offer a systematic survey of the m
Integrable Systems
Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Integrable Systems write by N.J. Hitchin. This book was released on 2013-03-14. Integrable Systems available in PDF, EPUB and Kindle. Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.
