We solve the equations of predictive relativistic mechanics for the electromagnetic interaction of two structureless point charges, up to second order in the coupling constant $g=e_1{e}_2$, using as a subsidiary condition the Liénard-Wiechert formulas, for both the advanced and the retarded potentials, separately or in the time-reversal-invariant combination. Our general results reduce in the case of one-dimensional rectilinear motion to those obtained previously by Hill, which, as shown recently by Andersen and von Baeyer, are reliable in the low energy regime. In the time-reversal-invariant combination, if $g<\mathrm{}0\mathrm{}$, concentric circular motion is possible; and assuming that both charges have equal masses we compare the speed-vs-radius relation obtained in this theory to that obtained in the Breit-Darwin approximation and in Wheeler-Feynman electrodynamics.

• Received 2 October 1972

DOI:https://doi.org/10.1103/PhysRevD.7.1099