A Kaluza-Klein Reduction of Super-integrable Systems
arXiv:1801.02981 · doi:10.1016/j.geomphys.2018.05.014
Abstract
Given a super-integrable system in 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 dimensions. Remarkably, the isometries of the reduced space can be derived from those of the dimensional space, even though it requires the use of {\em quadratic} expressions in momenta.
12 pages. arXiv admin note: text overlap with arXiv:1711.10583