The force on a point charge source of the classical electromagnetic field

Abstract

It is shown that a well-defined expression for the total electromagnetic force $f^{em}$ on a point charge source of the classical electromagnetic field can be extracted from the postulate of total momentum conservation whenever the classical electromagnetic field theory satisfies a handful of regularity conditions. Amongst these is the generic local integrability of the field momentum density over a neighborhood of the point charge. This disqualifies the textbook Maxwell-Lorentz field equations, while the Maxwell-Bopp-Lande-Thomas-Podolsky field equations qualify, and presumably so do the Maxwell-Born-Infeld field equations. Most importantly, when the usual relativistic relation between the velocity and the momentum of a point charge with bare rest mass $m_b\ne 0$ is postulated, Newton's law $\dot{p}=f$ with $f=f^{em}$ becomes an integral equation for the point particle's acceleration; the infamous third-order time derivative of the position which plagues the Abraham-Lorentz-Dirac equation of motion does not show up. No infinite bare mass renormalization is invoked, and no ad hoc averaging of fields over a neighborhood of the point charge. The approach lays the rigorous microscopic foundations of classical electrodynamics.

Preprint with correction markings in color, implementing a separate erratum to the original paper which appeared in Phys. Rev. D. vol. 101, 109901(E) (2020)

References in corpus (2)

• A Rigorous Derivation of Electromagnetic Self-force
• Aspects of electromagnetic radiation reaction in strong fields

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