The electrodynamics of inhomogeneous rotating media and the Abraham and Minkowski tensors. I. General theory
The electrodynamics of inhomogeneous rotating media and the Abraham and Minkowski tensors. I. General theory
复制标题
DOI：
10.1098/rspa.2010.0110
复制
发表时间：
2010-03
期刊：
影响因子：
--
通讯作者：
S. Goto;R. Tucker;T. Walton
中科院分区：
文献类型：
--
作者：
S. Goto;R. Tucker;T. Walton
这是一系列的两篇论文中的第一篇，它对电磁应力-能量-动量张量在连续可极化完全绝缘介质的经典描述中的作用进行了独立的分析。在承认总应力-能量-动量张量在时空中所起的主要作用的同时，我们认为，在协变本构理论的背景下，当相对于特定的分裂定义时，将优先状态分配给这个总张量的特定部分是有意义和有用的。自闵可夫斯基、爱因斯坦、劳布和亚伯拉罕在世纪前考虑这些问题以来，张量（与麦克斯韦的极化介质方程中出现的电磁场有关）与它们诱导的力和扭矩的相关性一直是一个争论的问题。由这些张量的发散而产生的力密度的概念是相对于介质的某些惯性性质而严格定义的。与牛顿连续介质力学定律的一致性要求介质中任何单元上的合力密度与该单元在惯性系中的局部线性加速度场成比例，并且还必须作为总应力-能量-动量张量的发散的一部分出现。与闵可夫斯基提出的张量不同，亚伯拉罕张量的发散明确地取决于介质的局部加速度场以及电磁场，这一事实使它与介质的总应力-能量-动量张量中的许多其他项区分开来。在本文中，我们将探讨如何电磁力或力矩的运动介质可以定义协变的一个特定的3-形式的时空，表现出特定的Killing对称性。它示出了如何驱动形式与平移Killing矢量场导致明确的表达式的电磁力密度在固定介质的闵可夫斯基本构关系，这些与其他模型相比，涉及极化介质中的电磁场，已被认为是在最近的文献。
This is paper I of a series of two papers, offering a self-contained analysis of the role of electromagnetic stress–energy–momentum tensors in the classical description of continuous polarizable perfectly insulating media. While acknowledging the primary role played by the total stress–energy–momentum tensor on spacetime we argue that it is meaningful and useful in the context of covariant constitutive theory to assign preferred status to particular parts of this total tensor, when defined with respect to a particular splitting. The relevance of tensors, associated with the electromagnetic fields that appear in Maxwell’s equations for polarizable media, to the forces and torques that they induce has been a matter of some debate since Minkowski, Einstein and Laub, and Abraham considered these issues over a century ago. The notion of a force density that arises from the divergence of these tensors is strictly defined relative to some inertial property of the medium. Consistency with the laws of Newtonian continuum mechanics demands that the total force density on any element of a medium be proportional to the local linear acceleration field of that element in an inertial frame and must also arise as part of the divergence of the total stress–energy–momentum tensor. The fact that, unlike the tensor proposed by Minkowski, the divergence of the Abraham tensor depends explicitly on the local acceleration field of the medium as well as the electromagnetic field sets it apart from many other terms in the total stress–energy–momentum tensor for a medium. In this paper, we explore how electromagnetic forces or torques on moving media can be defined covariantly in terms of a particular 3-form on those spacetimes that exhibit particular Killing symmetries. It is shown how the drive-forms associated with translational Killing vector fields lead to explicit expressions for the electromagnetic force densities in stationary media subject to the Minkowski constitutive relations and these are compared with other models involving polarizable media in electromagnetic fields that have been considered in the recent literature.