Аннотация:
We describe a procedure to construct polynomial in the momenta first integrals of arbitrarily high degree for natural Hamiltonians H obtained as one-dimensional extensions of natural (geodesic) n-dimensional Hamiltonians L. The Liouville integrability of L implies the (minimal) superintegrability of H. We prove that, as a consequence of natural integrability conditions, it is necessary for the construction that the curvature of the metric tensor associated with L is constant. As examples, the procedure is applied to one-dimensional L, including and improving earlier results, and to two and three-dimensional L, providing new superintegrable systems.
Образец цитирования:
Claudia Chanu, Luca Degiovanni, Giovanni Rastelli, “First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator”, SIGMA, 7 (2011), 038, 12 pp.
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\by Claudia Chanu, Luca Degiovanni, Giovanni Rastelli
\paper First Integrals of Extended Hamiltonians in $n+1$ Dimensions Generated by Powers of an Operator
\jour SIGMA
\yr 2011
\vol 7
\papernumber 038
\totalpages 12
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\crossref{https://doi.org/10.3842/SIGMA.2011.038}
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Эта публикация цитируется в следующих 15 статьяx:
К. М. Кьяну, Д. Растелли, “Расширение необычных гамильтонианов”, ТМФ, 204:3 (2020), 321–331; C. M. Chanu, G. Rastelli, “Extensions of nonnatural Hamiltonians”, Theoret. and Math. Phys., 204:3 (2020), 1101–1109
Claudia Maria Chanu, Giovanni Rastelli, “On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces”, SIGMA, 16 (2020), 052, 16 pp.
Escobar-Ruiz A.M. Lopez Vieyra J.C. Winternitz P. Yurdusen I., “Fourth-Order Superintegrable Systems Separating in Polar Coordinates. II. Standard Potentials”, J. Phys. A-Math. Theor., 51:45 (2018), 455202
Chanu C.M. Degiovanni L. Rastelli G., “Modified Laplace–Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion”, J. Math. Phys., 58:3 (2017), 033509
Carinena J.F. Herranz F.J. Ranada M.F., “Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability”, J. Math. Phys., 58:2 (2017), 022701
Escobar-Ruiz A.M. Lopez Vieyra J.C. Winternitz P., “Fourth Order Superintegrable Systems Separating in Polar Coordinates. i. Exotic Potentials”, J. Phys. A-Math. Theor., 50:49 (2017), 495206
Chanu C.M. Rastelli G., “Extended Hamiltonians and Shift, Ladder Functions and Operators”, Ann. Phys., 386 (2017), 254–274
Chanu C.M., Degiovanni L., Rastelli G., “Warped Product of Hamiltonians and Extensions of Hamiltonian Systems”, Xxxth International Colloquium on Group Theoretical Methods in Physics (Icgtmp) (Group30), Journal of Physics Conference Series, 597, IOP Publishing Ltd, 2015, 012024
Ranada M.F., “The Tremblay–Turbiner–Winternitz System on Spherical and Hyperbolic Spaces: Superintegrability, Curvature-Dependent Formalism and Complex Factorization”, J. Phys. A-Math. Theor., 47:16 (2014), 165203
Rastelli G., “Extensions of Natural Hamiltonians”, 2nd International Conference on Mathematical Modeling in Physical Sciences 2013 (Ic-Msquare 2013), Journal of Physics Conference Series, 490, eds. Vagenas E., Vlachos D., IOP Publishing Ltd, 2014, 012088
Chanu C.M., Degiovanni L., Rastelli G., “The Tremblay–Turbiner–Winternitz System as Extended Hamiltonian”, J. Math. Phys., 55:12 (2014), 122701
Chanu C.M., Degiovanni L., Rastelli G., “Extensions of Hamiltonian Systems Dependent on a Rational Parameter”, J. Math. Phys., 55:12 (2014), 122703
Claudia M. Chanu, Luca Degiovanni, Giovanni Rastelli, “Superintegrable extensions of superintegrable systems”, SIGMA, 8 (2012), 070, 12 pp.
Chanu C., Degiovanni L., Rastelli G., “Generalizations of a Method for Constructing First Integrals of a Class of Natural Hamiltonians and Some Remarks About Quantization”, 7th International Conference on Quantum Theory and Symmetries (Qts7), Journal of Physics Conference Series, 343, IOP Publishing Ltd, 2012, 012101
Chanu C., Degiovanni L., Rastelli G., “Three and Four-body Systems in One Dimension: Integrability, Superintegrability and Discrete Symmetries”, Regular & Chaotic Dynamics, 16:5 (2011), 496–503
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