Integrable systems, symmetries and quantization

Abstract

These notes correspond to a mini-course given at the Poisson 2016 conference in Geneva. Starting from classical integrable systems in the sense of Liouville, we explore the notion of non-degenerate singularity and expose recent research in connection with semi-toric systems. The quantum and semiclassical counterpart will also be presented, in the viewpoint of the inverse question: from the quantum mechanical spectrum, can you recover the classical system?

91 pages, 4 figures

References in corpus (3)

• Regular Poisson manifolds of compact types (PMCT 2)
• Vu Ngoc's Conjecture on focus-focus singular fibers with multiple pinched points
• Faithful Semitoric Systems

Cited by in corpus (11)

• Open Problems, Questions, and Challenges in Finite-Dimensional Integrable Systems
• Symplectic classification of coupled angular momenta
• First Integrals and symmetries of nonholonomic systems
• Vu Ngoc's Conjecture on focus-focus singular fibers with multiple pinched points
• Faithful Semitoric Systems
• Survey on recent developments in semitoric systems
• Integrability, Normal Forms, and Magnetic Axis Coordinates
• Quantum footprints of Liouville integrable systems
• Asymptotic Lattices, Good Labellings, and the Rotation Number for Quantum Integrable Systems
• The twisting index in semitoric systems
• Differential spaces in integrable Hamiltonian systems