论文标题
基于Riemann-Silberstein-Weber矢量的麦克斯韦方程的新矩阵表示，用于线性不均匀培养基
A new matrix representation of the Maxwell equations based on the Riemann-Silberstein-Weber vector for a linear inhomogeneous medium
论文作者
论文摘要
我们为线性均匀介质的麦克斯韦方程的新八维矩阵表示，并将其扩展到线性含量含量介质的情况。该派生从麦克斯韦方程式开始，并根据保利矩阵的代数使用参数。此过程将基于Riemann-Silberstein-Weber（RSW）向量自动导致矩阵表示。同质介质的新表示形式是四个Pauli矩阵块的直接总和。新表示的这一方面应该使其适合于在线性不均匀培养基中研究电磁波的传播，该介质采用量子力学技术，将不均匀性作为扰动。新表示形式用于重新等级Mukunda-Simon-Sudarshan矩阵替代规则，用于从Helmholtz标量波光学元件过渡到Maxwell Vector Wave Optics。
We derive a new eight dimensional matrix representation of the Maxwell equations for a linear homogeneous medium and extend it to the case of a linear inhomogneous medium. This derivation starts ab initio with the Maxwell equations and uses arguments based on the algebra of the Pauli matrices. This process leads automatically to the matrix representation based on the Riemann-Silberstein-Weber (RSW) vector. The new representation for the homogeneous medium is a direct sum of four Pauli matrix blocks. This aspect of the new representation should make it suitable for studying the propagation of electromagnetic waves in a linear inhomogeneous medium adopting the techniques of quantum mechanics treating the inhomogeneity as a perturbation. The new representation is used to rederive the Mukunda-Simon-Sudarshan matrix substitution rule for transition from the Helmholtz scalar wave optics to the Maxwell vector wave optics.
