Radiation reaction and renormalization in 2+1 electrodynamics
A self-action problem for a point-like charged particle arbitrarily moving in flat spacetime of three dimensions is considered. Outgoing waves carry energy-momentum and angular momentum; the radiation removes energy and angular momentum from the source which then undergoes a radiation reaction. We decompose Noether quantities carried by electromagnetic field into bound and radiative components. The bound terms are absorbed by individual particle's characteristics within the renormalization procedure. Radiative terms together with already renormalized three-momentum and angular momentum of point-like charge constitute the total conserved quantities of our particle plus field system. Their differential consequences yield the effective equation of motion of radiating charge in an external electromagnetic field. In this integro-differential equation the radiation back-reaction is determined by work done by Lorentz force of point-like charge acting upon itself plus non-local term which provides finiteness of the self-action.