Overview
- Gives a comprehensive introduction into basic aspects of integrability phenomenon
- Provides an extensive treatment of representative models both at classical and quantum level with a large amount of detailed derivations
- Covers modern theoretical techniques for finding exact solutions of an integrable model
Part of the book series: UNITEXT for Physics (UNITEXTPH)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (6 chapters)
Keywords
About this book
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 andRuijsenaars-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.
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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Elements of Classical and Quantum Integrable Systems
Authors: Gleb Arutyunov
Series Title: UNITEXT for Physics
DOI: https://doi.org/10.1007/978-3-030-24198-8
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-24197-1Published: 07 August 2019
Softcover ISBN: 978-3-030-24200-8Published: 15 August 2020
eBook ISBN: 978-3-030-24198-8Published: 23 July 2019
Series ISSN: 2198-7882
Series E-ISSN: 2198-7890
Edition Number: 1
Number of Pages: XIII, 414
Number of Illustrations: 31 b/w illustrations, 20 illustrations in colour
Topics: Statistical Physics and Dynamical Systems, Mathematical Physics, Classical Mechanics, Dynamical Systems and Ergodic Theory