Superintegrability and geometry: a review of the extended Hamiltonian approach
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913591466131456 |
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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 |