论文标题
第二梯度电动力学：一种非单明性相对论场理论
Second gradient electrodynamics: a non-singular relativistic field theory
论文作者
论文摘要
在本文中，我们给出了第二梯度电动力学的协变量，这是二阶的广义电动力学，包括高阶的衍生物。提出了场方程，能量量张量和洛伦兹力量密度的相对论形式。对于电点电荷，将广义的Lienard-Wiechert电势和相应的电磁场强度张量作为智障积分表达式。在没有任何奇异性和不连续性的情况下发现了电磁电位矢量和电磁场强度张量的明确公式。此外，给出了带电点粒子自我的世界线积分表达式。带电粒子的相对论运动方程与第二梯度电动力学中的电磁场相结合，这是一个及时非局部性的全差分方程。对于均匀加速的电荷，给出了自力有值的显式公式和无象征性的电磁质量。此外，分析了第二梯度电动力学真空中的波传播和分散关系。发现了三种波的模式：一个非分散性波，如麦克斯韦电动力学中，两个分散波与无碰撞血浆中的波传播相似。
In this paper, we give the covariant formulation of second gradient electrodynamics, which is a generalized electrodynamics of second order including derivatives of higher order. The relativistic form of the field equations, the energy-momentum tensor and the Lorentz force density are presented. For an electric point charge, the generalized Lienard-Wiechert potentials and the corresponding electromagnetic field strength tensor are given as retarded integral expressions. Explicit formulas for the electromagnetic potential vector and electromagnetic field strength tensor of a uniformly moving point charge are found without any singularity and discontinuity. In addition, a world-line integral expression for the self-force of a charged point particle is given. The relativistic equation of motion of a charged particle coupled with electromagnetic fields in second gradient electrodynamics is derived, which is an integro-differential equation with nonlocality in time. For a uniformly accelerated charge, explicit formulas of the self-force and the electromagnetic mass, being non-singular, are given. Moreover, the wave propagation and the dispersion relations in the vacuum of second gradient electrodynamics are analyzed. Three modes of waves were found: one non-dispersive wave as in Maxwell electrodynamics, and two dispersive waves similar to the wave propagation in a collisionless plasma.
