Integrability of Relativistic Dynamical Systems

In my presentation I will give a brief overview of our recent studies of relativistic dynamical systems. These are described by the Newton-Einstein-Lorentz equation generalising F = ma in the presence of external (electromagnetic) forces. I will explain how space-time and conformal symmetries may be employed to find conserved quantities that lead to integrability. In quite a few cases, the number of these quantities is surprisingly large implying super-integrability. This feature is somewhat ‘exotic’ due to its rare occurrence. For instance, by Bertrand’s theorem, in classical mechanics it only holds for the Kepler problem (with its Laplace-Runge-Lenz vector) and the harmonic oscillator. Using our generalised setting we have been able to extend this list significantly.