Superintegrability and geometry: a review of the extended Hamiltonian approach
Mathematical Physics
2024-12-02 v1 math.MP
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.
Keywords
Cite
@article{arxiv.2411.19815,
title = {Superintegrability and geometry: a review of the extended Hamiltonian approach},
author = {Claudia Maria Chanu and Giovanni Rastelli},
journal= {arXiv preprint arXiv:2411.19815},
year = {2024}
}
Comments
18 pages. arXiv admin note: text overlap with arXiv:1705.09519