Hidden symmetries of integrable conformal mechanical systems

Details Hidden symmetries of integrable conformal mechanical systems Hidden symmetries of integrable conformal mechanical systems

2009-08-23

arxiv.org/abs/0908.3290v1

Phys.Lett.A374:801-806,2010

Physics

High Energy Physics

High Energy Physics - Theory

9 pages revtex

Scientific paper

10.1016/j.physleta.2009.12.006

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;\alpha) symmetry.

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