  During the past century, there has been considerable discussion and analysis
of the motion of a point charge, taking into account "self-force" effects due
to the particle's own electromagnetic field. We analyze the issue of "particle
motion" in classical electromagnetism in a rigorous and systematic way by
considering a one-parameter family of solutions to the coupled Maxwell and
matter equations corresponding to having a body whose charge-current density
$J^a(\lambda)$ and stress-energy tensor $T_{ab} (\lambda)$ scale to zero size
in an asymptotically self-similar manner about a worldline $\gamma$ as $\lambda
\to 0$. In this limit, the charge, $q$, and total mass, $m$, of the body go to
zero, and $q/m$ goes to a well defined limit. The Maxwell field
$F_{ab}(\lambda)$ is assumed to be the retarded solution associated with
$J^a(\lambda)$ plus a homogeneous solution (the "external field") that varies
smoothly with $\lambda$. We prove that the worldline $\gamma$ must be a
solution to the Lorentz force equations of motion in the external field
$F_{ab}(\lambda=0)$. We then obtain self-force, dipole forces, and spin force
as first order perturbative corrections to the center of mass motion of the
body. We believe that this is the first rigorous derivation of the complete
first order correction to Lorentz force motion. We also address the issue of
obtaining a self-consistent perturbative equation of motion associated with our
perturbative result, and argue that the self-force equations of motion that
have previously been written down in conjunction with the "reduction of order"
procedure should provide accurate equations of motion for a sufficiently small
charged body with negligible dipole moments and spin. There is no corresponding
justification for the non-reduced-order equations.
