Superintegrability and geometry: a review of the extended Hamiltonian approach

2024/11/29 by Claudia Maria Chanu, Chanu, Claudia Maria, Giovanni Rastelli +1 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2411.19815

openalex publication_date 2024/11/29 · openalex created_date 2024/12/05 · openalex updated_date 2026/07/28

Abstract

We review the results of several of our papers about the procedure of extension of Hamiltonians, allowing the construction of families of superintegrable systems with non-trivial polynomial first integrals (or symmetry operators) of arbitrarily high degree. In particular, we focus on the geometric structures involved by the procedure: warped manifolds and Riemannian coverings. Examples of superintegrable systems, classical and quantum, with the structure of extended Hamiltonians are anisotropic harmonic oscillators, Kepler-Coulomb, Tremblay-Turbiner-Winternitz and Post-Winternitz systems.

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• The N-species integrable Volterra system as a maximally superintegrable Hamiltonian system

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