Superintegrability and geometry: a review of the extended Hamiltonian approach

Fuente: arXiv
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Main Authors: Chanu, Claudia Maria, Rastelli, Giovanni
Format: Preprint
Published: 2024
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author Chanu, Claudia Maria
Rastelli, Giovanni
author_facet Chanu, Claudia Maria
Rastelli, Giovanni
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2411_19815
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Superintegrability and geometry: a review of the extended Hamiltonian approach
Chanu, Claudia Maria
Rastelli, Giovanni
Mathematical Physics
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.
title Superintegrability and geometry: a review of the extended Hamiltonian approach
topic Mathematical Physics
url https://arxiv.org/abs/2411.19815