Maxwell–Lorentz without self-interactions: conservation of energy and momentum

Abstract

Since a classical charged point particle radiates energy and momentum it is argued that there must be a radiation reaction force. Here we present an action for the Maxwell–Lorentz without self-interactions model, where each particle only responds to the fields of the other charged particles. The corresponding stress–energy tensor automatically conserves energy and momentum in Minkowski and other appropriate spacetimes. Hence there is no need for any radiation reaction.