麦克斯韦场中相互作用电荷的慢运动
Slow Motion of Charges Interacting Through the Maxwell Field
摘要：
研究了$N$电荷与麦克斯韦场相互作用的Abraham模型。在装药直径$R_ϕ$的尺度上，装药间隔距离为$\eps^{-1}R_ϕ$，并且具有速度$\sqrt{\eps} c$，其中$\eps$是小的无量纲参数。我们遵循的运动的费用在时间的顺序$\eps^{-3/2}R_ϕ/c$，并证明在这个时间尺度上，他们的运动是很好的近似达尔文拉格朗日。质量被重整化。相互作用由瞬时库仑力主导，其量级为$\eps^{2}$。磁场和一阶延迟产生$\eps^{3}$阶的达尔文校正。辐射阻尼的数量级为$\eps^{7/2}$。
英文摘要：
We study the Abraham model for $N$ charges interacting with the Maxwell field. On the scale of the charge diameter, $R_ϕ$, the charges are a distance $\eps^{-1}R_ϕ$ 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 $\eps^{-3/2}R_ϕ/c$ 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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