Elements of Classical and Quantum Integrable Systems

1. Front Matter

   Pages i-xiii

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2. Liouville Integrability

   • Gleb Arutyunov

   Pages 1-68

3. Integrability from Symmetries

   • Gleb Arutyunov

   Pages 69-170

4. Quantum-Mechanical Integrable Systems

   • Gleb Arutyunov

   Pages 171-237

5. Factorised Scattering Theory

   • Gleb Arutyunov

   Pages 239-287

6. Bethe Ansatz

   • Gleb Arutyunov

   Pages 289-333

7. Integrable Thermodynamics

   • Gleb Arutyunov

   Pages 335-369

8. Back Matter

   Pages 371-414

   PDF

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.

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

“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)

• II Institute for Theoretical Physics, University of Hamburg, Hamburg, Germany

  Gleb Arutyunov

Dr. Gleb Arutyunov received his PhD in Theoretical Physics in 1996 from Steklov Mathematical Institute in Moscow. After completing his Alexander von Humboldt fellowship at Ludwig Maximilian University of Munich he became a postdoctoral fellow and then in 2002 a senior researcher at the Max-Planck Institute for Gravitational Physics (Albert Einstein Institute) in Potsdam. From 2005 he held various professor positions at the Institute for Theoretical Physics of Utrecht University. Since 2014 Dr. Arutyunov is a Professor of Mathematical Physics at  the University of Hamburg. His primary research interests include integrable models, quantum field and string theory. 

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