Hidden symmetries of integrable conformal mechanical systems |
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Authors: | Tigran Hakobyan Sergey Krivonos Armen Nersessian |
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Institution: | a Yerevan State University, 1 Alex Manoogian St., 0025 Yerevan, Armenia b Yerevan Physics Institute, 2 Alikhanyan Brothers St., 0036 Yerevan, Armenia c Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia d Institut für Theoretische Physik, Leibniz Universität Hannover, 30167 Hannover, Germany e Artsakh State University, 5 Mkhitar Gosh St., Stepanakert, Armenia |
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Abstract: | 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. |
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