A Kaluza-Klein Reduction of Super-integrable Systems

Allan P. Fordy

doi:10.1016/j.geomphys.2018.05.014

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arXiv · 1801.02981

A Kaluza-Klein Reduction of Super-integrable Systems

Allan P. Fordy

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Abstract

Given a super-integrable system in $n$ degrees of freedom, possessing an integral which is linear in momenta, we use the "Kaluza-Klein construction" in reverse to reduce to a lower dimensional super-integrable system. We give two examples of a reduction from 3 to 2 dimensions. The constant curvature metric (associated with the kinetic energy) is the same in both cases, but with two different super-integrable extensions. For these, we use different elements of the algebra of isometries of the kinetic energy to reduce to $2-$dimensions. Remarkably, the isometries of the reduced space can be derived from those of the $3-$dimensional space, even though it requires the use of {\em quadratic} expressions in momenta.

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Allan P. Fordy. 2018-01-06. A Kaluza-Klein Reduction of Super-integrable Systems. https://doi.org/10.1016/j.geomphys.2018.05.014

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