匀加速电荷电磁场的不连续性
A discontinuity in the electromagnetic field of a uniformly accelerated charge
摘要：
匀加速电荷的电场显示出一个不连续的平面，其中场仅在该平面的一侧延伸，在该平面上以有限值突然终止。这表明无源区域中的电场的非零发散，意味着违反高斯定律。为了使场处处符合麦克斯韦方程，需要一个与不连续平面上的$δ$函数成比例的附加场分量。这样的“$δ$场”可能是电荷的电磁场，在施加无限大的加速度之前，以接近$c$（光速）的匀速运动。然而，为这种情况导出该$δ$字段的一些尝试没有完全成功。一些推导的主张涉及到一些不那么明显的数学近似的精心计算。由于要导出的结果是已知的，从它符合麦克斯韦方程组的约束，和推导涉及熟悉的教科书表达式的领域，一个均匀运动的电荷，人们会期望一个容易，简单的方法，导致正确的结果。在这里，从一个均匀加速的电荷在瞬时静止帧的电磁场开始，在延迟时间的电荷的位置和运动方面，我们推导出这个$δ$ -场，符合麦克斯韦方程组，在一个相当简单的方式。接下来是计算的能量在$δ$ -场，在分析的方式，而不作任何近似，我们表明，这个能量正是一个将失去的电荷，因为辐射反应的电荷，成比例的变化率的加速度，这是强加给它在遥远的过去。
英文摘要：
The electric field of a uniformly accelerated charge shows a plane of discontinuity, where the field extending only on one side of the plane, terminates abruptly on the plane with a finite value. This indicates a non-zero divergence of the electric field in a source-free region, implying a violation of Gauss law. In order to make the field compliant with Maxwell's equations everywhere, an additional field component, proportional to a $δ$-function at the plane of discontinuity, is required. Such a "$δ$-field" might be the electromagnetic field of the charge, moving with a uniform velocity approaching $c$, the speed of light, prior to the imposition of acceleration at infinity. However, some attempts to derive this $δ$-field for such a case, have not been entirely successful. Some of the claims of the derivation involve elaborate calculations with some not-so-obvious mathematical approximations. Since the result to be derived is already known from the constraint of its compliance with Maxwell's equations, and the derivation involves the familiar text-book expressions for the field of a uniformly moving charge, one would expect an easy, simple approach, to lead to the correct result. Here, starting from the electromagnetic field of a uniformly accelerated charge in the instantaneous rest frame, in terms of the position and motion of the charge at the retarded time, we derive this $δ$-field, consistent with Maxwell's equations, in a fairly simple manner. This is followed by a calculation of the energy in the $δ$-field, in an analytical manner without making any approximation, where we show that this energy is exactly the one that would be lost by the charge because of the radiation reaction on the charge, proportional to its rate of change of acceleration, that was imposed on it at a distant past.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
