Hidden symmetries of integrable conformal mechanical systems

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.

9 pages revtex

References in corpus (8)

• Physics and Mathematics of Calogero particles
• N=4 superconformal Calogero models
• Calogero models and nonlocal conformal transformations
• N=4 mechanics, WDVV equations and roots
• Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space
• N=4 supersymmetric 3-particles Calogero model
• Lobachevsky geometry of (super)conformal mechanics
• WDVV solutions from orthocentric polytopes and Veselov systems

Cited by in corpus (55)

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• Integrable generalizations of oscillator and Coulomb systems via action-angle variables
• Invariants of the spherical sector in conformal mechanics
• Conformal mechanics inspired by extremal black holes in d=4
• Near horizon black holes in diverse dimensions and integrable models
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• Spherical Calogero model with oscillator/Coulomb potential: quantum case
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• Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"
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• Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems
• Near horizon extremal Myers-Perry black holes and integrability of associated conformal mechanics
• N=2 supersymmetric particle near extreme Kerr throat
• Couplings in D(2,1;a) superconformal mechanics from the SU(2) perspective
• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems
• The structure of invariants in conformal mechanics
• New realizations of the supergroup D(2,1;α) in N=4 superconformal mechanics
• On integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions
• Spherical Calogero model with oscillator/Coulomb potential: classical case
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• Integrable models associated with Myers-Perry-AdS-dS black hole in diverse dimensions
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• Integrability of the geodesic flow on the resolved conifolds over Sasaki-Einstein space $T^{1,1}$
• Dynamical symmetries of the Calogero-Coulomb model
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models