2009/08/23 by Tigran Hakobyan, S. Krivonos, Sergey Krivonos +2 · 5 citations
Chemistry · Mathematics · Physics and Astronomy · #Casimir effect #Classical mechanics #Conformal field theory #Conformal map #Conformal symmetry #Geometry #Hamiltonian (control theory) #Hamiltonian system #Homogeneous space #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Physics #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/j.physleta.2009.12.006
published as Phys.Lett.A374:801-806,2010 · 9 pages revtex
arxiv created 2009/08/23 · openalex publication_date 2009/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We split the generic conformal mechanical system into a "radial" and an "angular" part, where the latter is defined as the Hamiltonian system on the orbit of the conformal group, with the Casimir function in the role of the Hamiltonian. We reduce the analysis of the constants of motion of the full system to the study of certain differential equations on this orbit. For integrable mechanical systems, the conformal invariance renders them superintegrable, yielding an additional series of conserved quantities originally found by Wojciechowski in the rational Calogero model. Finally, we show that, starting from any N=4 supersymmetric "angular" Hamiltonian system one may construct a new system with full N=4 superconformal D(1,2;α) symmetry.