Lorentz group Lie algebra map of ultra-relativistic radiating electron

This paper discusses a precise numerical integrator for ultra-relativistic radiating electron motion. It is firstly shown that the covariant form Lorentz force equation of motion possesses the Lorentz group Lie algebra structure and the Lorentz-Dirac equation of motion as well. After that, a precise numerical integrator for radiating electron is constructed based on the Lie algebra properties. Numerical examples show that this integrator can be effectively used not only for the ultra-relativistic electron motion but also for a non-relativistic electron motions in pure magnetic fields as well