标题： Stückelberg-Horwitz-Piron 电动力学中的静电学 显示英文标题

标题： Electrostatics in Stueckelberg-Horwitz-Piron Electrodynamics

摘要： 本文中，我们研究了作为Stückelberg-Horwitz电磁理论特例的静电力学基本方面。在该理论中，时空事件$x^\mu(\tau)$在一个不受约束的8维相空间中演化，并通过由它们演化相关的电流密度诱导出的五个$\tau$-依赖规范场相互作用。为了使实验室时钟$x^0$根据能量的符号交替地“向前”和“向后”演化以实现时间，引入了时序时间$\tau$作为一个独立的演化参数，从而提供了Feynman-Stückelberg对粒子-反粒子产生/湮灭的经典实现。由此产生的理论在基础力学上不同于传统的电磁学，但在平衡极限下与麦克斯韦理论一致。在简要回顾了Stückelberg-Horwitz电动力学之后，我们得到了均匀运动事件所产生的场，并验证它满足场方程。我们在事件的静止参考系中研究这个场，它明确地依赖于坐标时间$x^0$和参数$\tau$，以及空间距离$R$。用这个广义的库仑场计算，我们展示了高斯定理和斯托克斯定理如何应用于4维时空，并得到带电线和带电面的场。最后，我们使用带电面的场来研究靠近势垒的静态事件。在所有这些情况下，我们都观察到场与粒子之间存在少量的质量转移。可以看出，对于处于足够密集的相反电荷面场中的事件，事件可以逆转时间方向，为粒子现象提供了一个具体模型。 显示英文摘要

摘要： In this paper, we study fundamental aspects of electrostatics as a special case in Stueckelberg-Horwitz electromagnetic theory. In this theory, spacetime events $x^\mu(\tau)$ evolve in an unconstrained 8-dimensional phase space, interacting through five $\tau$-dependent gauge fields induced by the current densities associated with their evolutions. The chronological time $\tau$ was introduced as an independent evolution parameter in order to free the laboratory clock $x^0$ to evolve alternately 'forward' and 'backward' in time according to the sign of the energy, thus providing a classical implementation of the Feynman-Stueckelberg interpretation of pair creation/annihilation. The resulting theory differs in its underlying mechanics from conventional electromagnetism, but coincides with Maxwell theory in an equilibrium limit. After a brief review of Stueckelberg-Horwitz electrodynamics, we obtain the field produced by an event in uniform motion and verify that it satisfies the field equations. We study this field in the rest frame of the event, where it depends explicitly on coordinate time $x^0$ and the parameter $\tau$, as well as spatial distance $R$. Calculating with this generalized Coulomb field, we demonstrate how Gauss's theorem and Stoke's theorem apply in 4D spacetime, and obtain the fields associated with a charged line and a charged sheet. Finally, we use the field of the charged sheet to study a static event in the vicinity of a potential barrier. In all of these cases, we observe a small transfer of mass from the field to the particle. It is seen that for an event in the field of an oppositely charged sheet of sufficient density, the event can reverse time direction, providing a specific model for pair phenomena.