任意运动点电荷上的自相互作用力及其相关的能量-动量辐射率的推导：Colombeau代数中的Lorentz-Dirac运动方程
Derivation of the self-interaction force on an arbitrarily moving point-charge and of its related energy-momentum radiation rate: The Lorentz-Dirac equation of motion in a Colombeau algebra
摘要：
经典理论的辐射点电荷被重新：推迟的潜力，场和电流被定义为非线性广义函数。所有的计算是在一个Colombeau代数，旋量表示所提供的双四元数制定的经典电动力学是用来使所有的四维积分准确和封闭的形式。任意运动的相对论性点电荷在其自身场的作用下辐射的能量动量的总速率严格等于减去该场的自相互作用力。这在不改变麦克斯韦理论的情况下，解决了一个多世纪以来许多长期存在的问题。作为直接应用，给出了洛伦兹-狄拉克运动方程的明确推导，并解释了肖特项问题的根源：这是由于点电荷的正确自能不是库仑自能，而是对δ平方函数的积分，该积分产生对肖特项的有限贡献，而肖特项在习惯公式中要么不存在，要么不正确。
英文摘要：
The classical theory of radiating point-charges is revisited: the retarded potentials, fields, and currents are defined as nonlinear generalized functions. All calculations are made in a Colombeau algebra, and the spinor representations provided by the biquaternion formulation of classical electrodynamics are used to make all four-dimensional integrations exactly and in closed-form. The total rate of energy-momentum radiated by an arbitrarily moving relativistic point-charge under the effect of its own field is shown to be rigorously equal to minus the self-interaction force due to that field. This solves, without changing anything in Maxwell's theory, numerous long-standing problems going back to more than a century. As an immediate application an unambiguous derivation of the Lorentz-Dirac equation of motion is given, and the origin of the problem with the Schott term is explained: it was due to the fact that the correct self-energy of a point charge is not the Coulomb self-energy, but an integral over a delta-squared function which yields a finite contribution to the Schott term that is either absent or incorrect in the customary formulations.
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