电磁变分法中速度不连续的极小元
Minimizers with discontinuous velocities for the electromagnetic variational method
摘要：
电磁二体问题具有\emph{neutral differential delay}运动方程，对于一般边界数据，该方程可以具有具有\emph{discontinuous}导数的解。如果要使用这些中立型时滞微分方程与\emph{arbitrary}边界数据，解决方案与不连续的衍生物必须是预期和允许的。令人惊讶的是，惠勒-费曼电动力学有一个边界值变分方法，其中最小轨迹与不连续的衍生物也是预期的，因为我们在这里显示。变分法定义连续轨迹，分段定义速度和加速度，电磁场定义\emph{by}欧拉-拉格朗日方程\emph{% on}轨迹点。在这里，我们使用分段定义的极小化与Li{é}nard-Wierchert公式来定义广义电磁场几乎无处不在（但在零测量点的集合上，超前/滞后速度和/或加速度是不连续的）。随着这一推广，我们制定的\emph{generalized absorber hypothesis}，远场渐近消失\emph{almost everywhere%}，并表明，本地化轨道与远场消失几乎无处不在\emph{must}有间断的速度缝链上的断点。通过求解一个关于零远场的中立型时滞微分方程，给出了零远场定域轨道的一般解。我们讨论了具有不连续导数的轨道的物理性质，强调了与经典力学的变分方法的不同，以及与广义变分电动力学相关的旋量四流的存在性。
英文摘要：
The electromagnetic two-body problem has \emph{neutral differential delay} equations of motion that, for generic boundary data, can have solutions with \emph{discontinuous} derivatives. If one wants to use these neutral differential delay equations with \emph{arbitrary} boundary data, solutions with discontinuous derivatives must be expected and allowed. Surprisingly, Wheeler-Feynman electrodynamics has a boundary value variational method for which minimizer trajectories with discontinuous derivatives are also expected, as we show here. The variational method defines continuous trajectories with piecewise defined velocities and accelerations, and electromagnetic fields defined \emph{by} the Euler-Lagrange equations \emph{% on} trajectory points. Here we use the piecewise defined minimizers with the Li{é}nard-Wierchert formulas to define generalized electromagnetic fields almost everywhere (but on sets of points of zero measure where the advanced/retarded velocities and/or accelerations are discontinuous). Along with this generalization we formulate the \emph{generalized absorber hypothesis} that the far fields vanish asymptotically \emph{almost everywhere%} and show that localized orbits with far fields vanishing almost everywhere \emph{must} have discontinuous velocities on sewing chains of breaking points. We give the general solution for localized orbits with vanishing far fields by solving a (linear) neutral differential delay equation for these far fields. We discuss the physics of orbits with discontinuous derivatives stressing the differences to the variational methods of classical mechanics and the existence of a spinorial four-current associated with the generalized variational electrodynamics.
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。
