Dynamical Symmetry

A symmetry that couples the kinetic and potential energy parts of the Hamiltonian is known as a dynamical symmetry.The most studied dynamical symmetry is probably that associated with the Kepler problem. In the non-relativistic Kepler problem, the symmetry manifests itself through the so-called Runge-Lenz vector which is a constant of the motion - both in classical mechanics and in quantum mechanics. In the relativistic Kepler problem, the Runge-Lenz vector ceases to be a constant of the motion. The removal of the dynamical symmetry is, however, not complete. The relativistic symmetry is accounted for by means of a constant of the motion originally introduced by Johnson and Lippmann.
The present project is concerned with salient aspects of both the non-relativistic and the relativistic Kepler problem.
The project is partly financed by a grant from The Danish Natural Sciences Research Council (SNF).