投影算子在电动力学中的应用
On the use of projection operators in electrodynamics
摘要：
在经典电动力学中，所有可测量的量都可以从规范不变的法拉第张量$F_{αβ}$导出。尽管如此，使用规范相关变量通常是有利的。文[4]、[2]、[8]及本文也讨论了Lorenz规范中矢势到Coulomb规范中矢势的变换。这种变换可以通过应用提取空间向量的横向部分的投影算子来完成。在许多情况下，适当的投影算子被简化的横投影算子所代替。人们普遍认为，这种替换不会影响辐射区的结果。本文将利用移动点装药的具体例子，比较适当的和简化的横向投影的作用。本文将证明，只要源的无限空间运动相对于观测者的参考系是无界的，用简化的横投影算符代替真投影算符，即使在辐射区，也会得到一个错误的结果，其误差与真库仑规范矢势本身的误差量级相同。
英文摘要：
In classical electrodynamics all the measurable quantities can be derived from the gauge invariant Faraday tensor $F_{αβ}$. Nevertheless, it is often advantageous to work with gauge dependent variables. In [4],[2] and [8], and in the present note too, the transformation of the vector potential in Lorenz gauge to that in Coulomb gauge is considered. This transformation can be done by applying a projection operator that extracts the transverse part of spatial vectors. In many circumstances the proper projection operator is replaced by a simplified transverse one. It is widely held that such a replacement does not affect the result in the radiation zone. In this paper the action of the proper and simplified transverse projections will be compared by making use of specific examples of a moving point charge. It will be demonstrated that whenever the interminable spatial motion of the source is unbounded with respect to the reference frame of the observer the replacement of the proper projection operator by the simplified transverse one yields, even in the radiation zone, an erroneous result with error which is of the same order as the proper Coulomb gauge vector potential itself.
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。
