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Approximate Solutions of Predictive Relativistic Mechanics for the Electromagnetic Interaction
Phys. Rev. D 7, 1099 – Published 15 February, 1973
DOI: https://doi.org/10.1103/PhysRevD.7.1099
Abstract
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 , 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 , 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.
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