第二梯度电动力学：格林函数，波传播，正则化和自作用力
Second gradient electrodynamics: Green functions, wave propagation, regularization and self-force
摘要：
在这项工作中，第二梯度电动力学，这是广义电动力学的一个重要例子的理论，提出和研究。第二梯度电动力学是一种梯度场论，其电磁场强度在拉格朗日密度中具有高达二阶导数。第二梯度电动力学在空间和时间上具有弱非定域性。在第二梯度电动力学的框架下，导出了三维、二维和一维空间的推迟格林函数、推迟格林函数的一阶导数、推迟势、推迟电磁场强度、广义Lienard-Wiechert势和相应的电磁场强度。研究了光锥上电磁场的行为。特别是，延迟格林函数和他们的一阶导数表现出振荡的经典解决方案内的前向光锥，它表明，他们是奇性自由和规则的光锥在三维，二维和一维空间。在第二梯度电动力学中，计算自作用力和能量释放率，并确定带电点粒子的运动方程，该运动方程是积分微分方程，其中不出现臭名昭著的位置的三阶时间导数。
英文摘要：
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.
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