电磁自作用力的严格推导
A Rigorous Derivation of Electromagnetic Self-force
摘要：
在过去的一个世纪里，人们对点电荷的运动进行了大量的讨论和分析，并考虑了由于粒子自身电磁场而产生的“自作用力”效应。我们分析了经典电磁学中的“粒子运动”问题，在一个严格和系统的方式，考虑一个参数的家庭的解决方案，耦合麦克斯韦方程和物质方程对应于有一个机构的电荷-电流密度$J^a(λ)$和应力-能量张量$T_{ab} (λ)$规模为零的大小在一个渐近自相似的方式关于世界线$γ$为$λ\to 0$。在这个极限中，物体的电荷$q$和总质量$m$都为零，而$q/m$也达到一个明确的极限。麦克斯韦场$F_{ab}(λ)$被假定为与$J^a(λ)$相关联的延迟解加上随$λ$平滑变化的齐次解（“外场”）。我们证明了世界线$γ$一定是洛伦兹力运动方程在外场$F_{ab}(λ=0)$中的解。然后，我们得到的自我力，偶极力，和自旋力作为一阶微扰修正的质量中心运动的身体。我们相信，这是第一次严格推导出完整的一阶修正洛仑兹力运动。我们还解决的问题，获得一个自洽的微扰运动方程与我们的微扰的结果，并认为，自作用力的运动方程，以前已经写下来的“减少订单”的程序应提供准确的运动方程为一个足够小的带电体，可以忽略不计的偶极矩和自旋。对于非降阶方程没有相应的证明。
英文摘要：
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 $J^a(λ)$ and stress-energy tensor $T_{ab} (λ)$ scale to zero size in an asymptotically self-similar manner about a worldline $γ$ as $λ\to 0$. 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 $F_{ab}(λ)$ is assumed to be the retarded solution associated with $J^a(λ)$ plus a homogeneous solution (the "external field") that varies smoothly with $λ$. We prove that the worldline $γ$ must be a solution to the Lorentz force equations of motion in the external field $F_{ab}(λ=0)$. 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.
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