Completeness of superintegrability in two-dimensional constant-curvature spaces

2001/02/07 by E. G. Kalnins, J. M. Kress, G. S. Pogosyan +2 · 6 citations
Mathematics · Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1088/0305-4470/34/22/311

published as J. Phys. A: Math. Gen. 34 (2001) 4705-4720 · 23 pages, LaTeX

arxiv created 2001/02/07 · openalex publication_date 2001/05/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the Hamiltonians H=px2+ py2 +V(x,y) of all classical superintegrable systems in two dimensional complex Euclidean space with second-order constants of the motion. We similarly classify the superintegrable Hamiltonians H=J12+J22+ J32+V(x,y,z) on the complex 2-sphere where x2+y2+z2=1. This is achieved in all generality using properties of the complex Euclidean group and the complex orthogonal group.

Cited by

• Superintegrability in a two-dimensional space of nonconstant curvature
• Hamiltonians separable in Cartesian coordinates and third-order integrals of motion
• Necessary conditions for partial and super-integrability of Hamiltonian systems with homogeneous potentia
• Laplace equations, conformal superintegrability and Bôcher contractions
• Integrable and superintegrable quantum systems in a magnetic field
• Superintegrable systems in Darboux spaces

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