Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold

Details Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold

2004-12-16

arxiv.org/abs/math-ph/0412055v3

J. Math. Phys. 47, 042904 (2006)

Physics

Mathematical Physics

LaTeX, 72 pages. Extended version of the published version in JMP

Scientific paper

In this paper we prove that the two dimensional superintegrable systems with quadratic integrals of motion on a manifold can be classified by using the Poisson algebra of the integrals of motion. There are six general fundamental classes of superintegrable systems. Analytic formulas for the involved integrals are calculated in all the cases. All the known superintegrable systems are classified as special cases of these six general classes.

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