Arutyunov G. Elements of Classical and Quantum Integrable Systems

Springer, 2019. — 420 p. — (UNITEXT for Physics). — ISBN: 978-3-030-24197-1.Integrable models have a fascinating history with manyimportant 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.Liouville Integrability
Integrability from Symmetries
Quantum-Mechanical Integrable Systems
Factorised Scattering Theory
Bethe Ansatz
Integrable Thermodynamics
Appendixes
Frobenius Theorem
Jacobi Identity for the Dirac Bracket
Details on the Double
Details on RS Models