Radiation reaction in 2 + 1 electrodynamics

A self-action problem for a pointlike charged particle arbitrarily moving in flat space-time of three dimensions is considered. Outgoing waves carry energy-momentum and angular momentum; the radiation removes energy, momentum, 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 3-momentum and angular momentum of pointlike 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 integrodifferential equation the radiation reaction is determined by Lorentz force of pointlike charge acting upon itself plus nonlocal term which provides finiteness of the self-action.