  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 $m_b \neq 0$ 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.
