Elements of Classical and Quantum Integrable Systems

  • Gleb Arutyunov

Part of the UNITEXT for Physics book series (UNITEXTPH)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Gleb Arutyunov
    Pages 1-68
  3. Gleb Arutyunov
    Pages 69-170
  4. Gleb Arutyunov
    Pages 171-237
  5. Gleb Arutyunov
    Pages 239-287
  6. Gleb Arutyunov
    Pages 289-333
  7. Gleb Arutyunov
    Pages 335-369
  8. Back Matter
    Pages 371-414

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 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 theory Weyl symmetry Moving coordinate systems n-body problem Bethe Ansatz Kolmogorov–Arnold–Moser theorem

Authors and affiliations

  • Gleb Arutyunov
    • 1
  1. 1.II Institute for Theoretical PhysicsUniversity of HamburgHamburgGermany

Bibliographic information