论文标题
第二梯度电动力学：绿色功能，波传播，正则化和自我强制
Second gradient electrodynamics: Green functions, wave propagation, regularization and self-force
论文作者
论文摘要
在这项工作中，提出和研究了第二梯度电动力学的理论，是广义电动力学的重要例子。第二梯度电动力学是一种梯度场理论，具有拉格朗日密度中电磁场强度的二阶导数。第二梯度电动力学在空间和时间上具有较弱的非局部性。在第二梯度电动力学的框架中，延迟的绿色功能，延迟的绿色功能的一阶导数，智障电位，延迟的电磁场强度，广义的Lienard-Wiechert电位以及相应的电磁场强度为三个，两个和一个空间维度衍生而成。在光锥上研究了电磁场的行为。特别是，延迟的绿色功能及其第一阶导数显示了前灯锥体内的经典溶液周围的振荡，并且表明它们在三个，两个和一个空间维度中不含奇异性，并且在光锥上进行固定。在第二个梯度电动力学中，计算自力和能量释放速率，并确定带电点粒子的运动方程，这是一个不差异的方程，其中未出现臭名昭著的三阶时间衍生物。
In this work, the theory of second gradient electrodynamics, which is an important example of generalized electrodynamics, is proposed and investigated. Second gradient electrodynamics is a gradient field theory with up to second-order derivatives of the electromagnetic field strengths in the Lagrangian density. Second gradient electrodynamics possesses a weak nonlocality in space and time. In the framework of second gradient electrodynamics, the retarded Green functions, first-order derivatives of the retarded Green functions, retarded potentials, retarded electromagnetic field strengths, generalized Lienard-Wiechert potentials and the corresponding electromagnetic field strengths are derived for three, two and one spatial dimensions. The behaviour of the electromagnetic fields is investigated on the light cone. In particular, the retarded Green functions and their first-order derivatives show oscillations around the classical solutions inside the forward light cone and it is shown that they are singularity-free and regular on the light cone in three, two and one spatial dimensions. In second gradient electrodynamics, the self-force and the energy release rate are calculated and the equation of motion of a charged point particle, which is an integro-differential equation where the infamous third-order time-derivative of the position does not appear, is determined.
