Interactions in Crystals by a Lagrangian Approach

任意介电晶体与电磁场相互作用的拉克斯-尼尔森拉格朗日理论将应用于几种相互作用。弹性光学效应将在接近二阶相变的晶体中进行研究。这将探讨如何测量线性弹性刚度张量的不对称性，该张量是由旋转耦合产生的，最近由该理论预测。该理论最近的预测是，自然光学活性可以在晶体中形成三种不同的机制，并产生具有两种频散类型的项，将扩展到磁诱导光学活性（法拉第效应）。光学活性的声学模拟，声活性也将进行探讨。计算由应力或电场作用引起的光学模式的频移，并将其与弹光效应联系起来。我们将根据在空间坐标系和物质坐标系中分别表示的实动量和伪动量的一般守恒定律，以及我们先前对介电晶体与电磁场相互作用的一般非线性应力张量的分析，提出闵可夫斯基-亚伯拉罕争议的解决办法。拉格朗日理论将被推广到包括组成晶格的粒子的本征自旋。这将允许处理铁磁和铁磁相互作用。这将通过引入Grassman变量来实现。

The Lax-Nelson Lagrangian theory of an arbitrary dielectric crystal in interaction with the electromagnetic field will be applied to several interactions. The elastooptic effect will be studied in a crystal near a second-order phase transition. This will explore how the asymmetry of the linear elastic stiffness tensor, produced by coupling to rotation and recently predicted by this theory, can be measured. The recent prediction of this theory that natural optical activity can arise form three distinct mechanisms in crystals and produce terms having two types of frequency dispersion will be extended to magnetically induced optical activity (Faraday effect). The acoustic analog of optical activity, acoustic activity will also be explored. The frequency shift of optic modes caused by the application of stress or an electric field will be calculated and related to the elastooptic effect. A resolution to the Minkowski-Abraham controversy will be presented based on the general conservation laws of real momentum and pseudo-momentum expressed in the spatial and material coordinate systems respectively and upon our previous analysis of the general nonlinear stress tensor of a dielectric crystal in interaction with the electromagnetic field. The Lagrangian theory will be generalized to include intrinsic spin of the particles composing the crystal lattice. This will allow treatment of ferromagnetic and ferrimagnetic interactions. This will be accomplished by the introduction of Grassman variables.