第二梯度电磁学：电点电荷，静电与静磁偶极子
Second gradient electromagnetostatics: electric point charge, electrostatic and magnetostatic dipoles
摘要：
本文研究了作为第二梯度电动力学静态形式的第二梯度静电磁学理论。第二梯度电动力学理论是高阶经典麦克斯韦电动力学的线性推广，其拉格朗日量是洛伦兹和U（1）规范不变量。二阶梯度电磁静学是一种梯度场论，其电磁场强度在拉格朗日量中具有高达二阶导数。此外，它还具有弱的空间非局部性，并给出了一个基于高阶偏微分方程的正则化。从群论的角度来看，在第二梯度电磁静力学的（各向同性）本构关系涉及一个不变的标量微分算子的四阶除了标量本构参数。我们调查的经典静态问题的一个电点电荷，电和磁偶极子的第二梯度电磁静力学的框架，我们表明，所有的电磁场（电位，场强，相互作用能，相互作用力）是奇性自由不同于相应的解决方案，在经典的麦克斯韦电磁学以及在Bopp-Podolsky理论。二阶梯度静电磁场理论提供了一种具有弱空间非局域性的无奇性电磁场论。
英文摘要：
In this paper, we study the theory of second gradient electromagnetostatics as the static version of second gradient electrodynamics. The theory of second gradient electrodynamics is a linear generalization of higher order of classical Maxwell electrodynamics whose Lagrangian is both Lorentz and U(1)-gauge invariant. Second gradient electromagnetostatics is a gradient field theory with up to second-order derivatives of the electromagnetic field strengths in the Lagrangian. Moreover, it possesses a weak nonlocality in space and gives a regularization based on higher-order partial differential equations. From the group theoretical point of view, in second gradient electromagnetostatics the (isotropic) constitutive relations involve an invariant scalar differential operator of fourth order in addition to scalar constitutive parameters. We investigate the classical static problems of an electric point charge, and electric and magnetic dipoles in the framework of second gradient electromagnetostatics, and we show that all the electromagnetic fields (potential, field strength, interaction energy, interaction force) are singularity-free unlike the corresponding solutions in the classical Maxwell electromagnetism as well as in the Bopp-Podolsky theory. The theory of second gradient electromagnetostatics delivers a singularity-free electromagnetic field theory with weak spatial nonlocality.
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。
