论文标题
第二梯度电磁术：电点电荷，静电和磁静态偶极子
Second gradient electromagnetostatics: electric point charge, electrostatic and magnetostatic dipoles
论文作者
论文摘要
在本文中，我们研究了第二梯度电磁术作为第二梯度电动力学的静态版本的理论。第二梯度电动力学的理论是对经典麦克斯韦电动力学高阶的线性概括，其Lagrangian既是Lorentz又是U（1） - gauge不变。第二梯度电磁术是一种梯度场理论，具有拉格朗日电磁场强度的二阶导数。此外，它在空间中具有较弱的非局部性，并基于高阶偏微分方程提供了正则化。从组理论的角度来看，在第二梯度电磁术中，（各向同性）组成关系涉及第四顺序的不变标量差分运算符，除标量构成参数外。我们研究了电点电荷的经典静态问题，以及第二梯度电磁术的框架中的电和磁性偶极子，我们表明所有电磁场（潜在的，现场强度，相互作用，相互作用，相互作用力）都是无偶然性的，与古典Maxwell Electomagnetism中的相应解决方案不同，这是无偶然性的。第二梯度电磁静态学的理论提供了无奇异性电磁场理论，其空间非局部性弱。
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.
