Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2011-10-31
J. Phys.: Conf. Ser. 343 012101 (2012) (v1 version)
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Presented at the conference Quantum Theory and Symmetries 7, Praha, August 7-13 2011. In v2 some typos corrected, a comment ad
Scientific paper
In previous papers we determined necessary and sufficient conditions for the existence of a class of natural Hamiltonians with non-trivial first integrals of arbitrarily high degree in the momenta. Such Hamiltonians were characterized as (n+1)-dimensional extensions of n-dimensional Hamiltonians on constant-curvature (pseudo-)Riemannian manifolds Q. In this paper, we generalize that approach in various directions, we obtain an explicit expression for the first integrals, holding on the more general case of Hamiltonians on Poisson manifolds, and show how the construction of above is made possible by the existence on Q of particular conformal Killing tensors or, equivalently, particular conformal master symmetries of the geodesic equations. Finally, we consider the problem of Laplace-Beltrami quantization of these first integrals when they are of second-degree.
Chanu Claudia
Degiovanni Luca
Rastelli Giovanni
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