Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8255436 | Journal of Geometry and Physics | 2018 | 10 Pages |
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 quadratic expressions in momenta.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Allan P. Fordy,