Noncompact $\mathbf{CP}^N$ as a phase space of superintegrable systems

Erik Khastyan; Armen Nersessian; Hovhannes Shmavonyan

doi:10.1142/S0217751X2150055X

Noncompact $\mathbf{CP}^N$ as a phase space of superintegrable systems

Mathematical Physics 2025-04-04 v2 High Energy Physics - Theory math.MP

Authors: Erik Khastyan , Armen Nersessian , Hovhannes Shmavonyan

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Abstract

We propose the description of superintegrable models with dynamical $so(1.2)$ symmetry, and of the generic superintegrable deformations of oscillator and Coulomb systems in terms of higher-dimensional Klein model (the non-compact analog of complex projective space) playing the role of phase space. We present the expressions of the constants of motion of these systems via Killing potentials defining the $su(N.1)$ isometries of the K\"ahler structure.

Keywords

integrable hamiltonian systems calogero models supersymmetry

Cite

@article{arxiv.2003.10002,
  title  = {Noncompact $\mathbf{CP}^N$ as a phase space of superintegrable systems},
  author = {Erik Khastyan and Armen Nersessian and Hovhannes Shmavonyan},
  journal= {arXiv preprint arXiv:2003.10002},
  year   = {2025}
}