Self-force and synchrotron radiation in odd space-time dimensions

Classical electrodynamics in flat 3+1 space-time has a very special retarded propagator delta(x^2) localized on the light cone, so that a particle does not interact with its past field. However, this is an exception, and in flat odd-dimensional space-times as well as generic curved spaces this is not so. In this work we show that the so called self-force is not only non-zero, but it matches (in 2+1 dimensions) the radiation reaction force derived from the radiation intensity.