(Super)integrability from coalgebra symmetry: formalism and applications

Details (Super)integrability from coalgebra symmetry: formalism and applications (Super)integrability from coalgebra symmetry: formalism and applications

2009-05-08

arxiv.org/abs/0905.1298v1

J.Phys.Conf.Ser.175:012004,2009

Physics

Mathematical Physics

33 pages. Review-contribution to the "Workshop on higher symmetries in Physics", 6-8 November 2008, Madrid, Spain

Scientific paper

10.1088/1742-6596/175/1/012004

The coalgebra approach to the construction of classical integrable systems from Poisson coalgebras is reviewed, and the essential role played by symplectic realizations in this framework is emphasized. Many examples of Hamiltonians with either undeformed or q-deformed coalgebra symmetry are given, and their Liouville superintegrability is discussed. Among them, (quasi-maximally) superintegrable systems on N-dimensional curved spaces of nonconstant curvature are analysed in detail. Further generalizations of the coalgebra approach that make use of comodule and loop algebras are presented. The generalization of such a coalgebra symmetry framework to quantum mechanical systems is straightforward.

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