Abstract
This paper considers the relativistic motion of charged particles coupled with electromagnetic fields in the higher-order theory proposed by Bopp, Landé–Thomas, and Podolsky. We rigorously derive a world line integral expression for the self-force of the charged particle from a distributional equation for the conservation of four-momentum only. This naturally leads to an equation of motion for charged particles that incorporates a history-dependent self-interaction. We show additionally that the same equation of motion follows from a variational principle for retarded fields. Our work thus gives a rigorous vindication of an expression for the self-force first proposed by Landé and Thomas, studied by Zayats for straight line motion, and, more generally, obtained by Gratus, Perlick, and Tucker on the basis of an averaging axiom.
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