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PreprintCC BY 4.0arXiv

Equivalence of superintegrable Poisson projection chains: magnetic cotangent bundles and spin Calogero-Moser models

  • Kai Jiang
  • Guorui Ma
  • Junze Zhang
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Abstract

We study superintegrable Hamiltonian systems in terms of Poisson projection chains and their (spectral) equivalence. We compare two reduction constructions: (i) the cotangent bundle T*(G/A), A=ZG(γ), with the magnetic symplectic form defined by the orbit G· γ≅ G/A, and (ii) the left-right Hamiltonian reduction of T*G that gives spin Calogero-Moser type systems. We prove that the two resulting chains are equivalent on an open set of regular points of principal orbit type: the phase spaces, the intermediate Poisson manifolds and the base spaces are identified compatibly with the projections. In particular, both constructions give the same commuting Hamiltonians.

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Cite

BibTeXRIS
BibTeX
@misc{jiang2026equivalence,
  title = {{Equivalence of superintegrable Poisson projection chains: magnetic cotangent bundles and spin Calogero-Moser models}},
  author = {Kai Jiang and Guorui Ma and Junze Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00992},
  eprint = {2611.00992},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00992},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Equivalence of superintegrable Poisson projection chains: magnetic cotangent bundles and spin Calogero-Moser models
AU  - Kai Jiang
AU  - Guorui Ma
AU  - Junze Zhang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00992
UR  - https://arxiv.org/abs/2611.00992
AB  - We study superintegrable Hamiltonian systems in terms of Poisson projection chains and their (spectral) equivalence. We compare two reduction constructions: (i) the cotangent bundle T^*(G/A), A=Z_G(γ), with the magnetic symplectic form defined by the orbit G· γ≅ G/A, and (ii) the left-right Hamiltonian reduction of T^*G that gives spin Calogero-Moser type systems. We prove that the two resulting chains are equivalent on an open set of regular points of principal orbit type: the phase spaces, the intermediate Poisson manifolds and the base spaces are identified compatibly with the projections. In particular, both constructions give the same commuting Hamiltonians.
ER  -