标题： 使用扩展物体方法计算自力 显示英文标题

标题： Calculation of the Self Force using the Extended-Object Approach

摘要： 我们在这里提出一种扩展物体方法，用于解释和计算自力现象。 在这种方法中，考虑一个具有有限尺寸$\epsilon$的带电扩展物体，它以非平凡的方式加速，并计算由电磁场（其源是该带电物体本身）作用在它上面的总力。 我们证明，在极限$\epsilon \to 0$时，这个总的电磁场产生一个与物体形状无关的普遍结果，这与点电荷所受的标准自力表达式一致。 这种方法已经被许多作者考虑过，但以前的分析最终得到的总电磁力表达式包含了$O(1/\epsilon)$项，这些项不符合质量重整化的形式要求。 （在球形电荷分布的特殊情况下，这项$\propto 1/\epsilon $被发现比所需的量大 4/3 倍。） 我们在这里表明，这个问题源于之前分析中对“总电磁力”概念的过于简单的定义。 基于能量动量守恒与适当的相对论运动学，我们推导出正确的总电磁力概念。 这完全解决了任何物体形状的有问题的$O(1/\epsilon)$项，并在极限$\epsilon \to 0$时给出了正确的自力。 特别是，对于球形电荷分布，上述“4/3 问题”得到了解决。 显示英文摘要

摘要： We present here the extended-object approach for the explanation and calculation of the self-force phenomenon. In this approach, one considers a charged extended object of a finite size $\epsilon$ that accelerates in a nontrivial manner, and calculates the total force exerted on it by the electromagnetic field (whose source is the charged object itself). We show that at the limit $\epsilon \to 0$ this overall electromagnetic field yields a universal result, independent on the object's shape, which agrees with the standard expression for the self force acting on a point-like charge. This approach has already been considered by many authors, but previous analyses ended up with expressions for the total electromagnetic force that include $O(1/\epsilon)$ terms which do not have the form required by mass-renormalization. (In the special case of a spherical charge distribution, this $\propto 1/\epsilon $ term was found to be 4/3 times larger than the desired quantity.) We show here that this problem was originated from a too naive definition of the notion of ''total electromagnetic force'' used in previous analyses. Based on energy-momentum conservation combined with proper relativistic kinematics, we derive here the correct notion of total electromagnetic force. This completely cures the problematic $O(1/\epsilon)$ term, for any object's shape, and yields the correct self force at the limit $\epsilon \to 0$. In particular, for a spherical charge distribution, the above ''4/3 problem'' is resolved.