Elements of Classical and Quantum Integrable Systems

By: Gleb Arutyunov

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Hardcover | 7 August 2019

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Hardcover
430 Pages

Dimensions(cm)
23.39 x 15.6 x 2.39

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$156.18

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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.

Industry Reviews

"This well-written and well thought out book deals with some marvelous material, which, while meant for physicists, and written by a physicist, is of great relevance to mathematics. This book should be very interesting and useful to many mathematicians." (Michael Berg, MAA Reviews, March 7, 2020)

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