 001 Markus Kunze, Herbert Spohn
 Slow Motion of Charges Interacting Through the Maxwell Field
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Jan 3, 00

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Abstract. We study the Abraham model for $N$ charges interacting with the Maxwell
field. On the scale of the charge diameter, $R_{\varphi}$, the charges
are a distance $\eps^{1}R_{\varphi}$ apart and have a velocity
$\sqrt{\eps} c$ with $\eps$ a small dimensionless parameter. We follow
the motion of the charges over times of the order
$\eps^{3/2}R_{\varphi}/c$ and prove that on this time scale their
motion is well approximated by the Darwin Lagrangian. The mass is
renormalized. The interaction is dominated by the instantaneous Coulomb
forces, which are of the order $\eps^{2}$. The magnetic fields and
first order retardation generate the Darwin correction of the order
$\eps^{3}$. Radiation damping would be of the order $\eps^{7/2}$.
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