基于矩阵的介质电动力学方法
Matrix-based approach to electrodynamics in media
摘要：
本文用矩阵形式研究了任意介质和电源条件下麦克斯韦电动力学的Riemann-Silberstein- Majorana - Oppenheimer方法。明确地证明了矩阵麦克斯韦方程在复转动群SO（3.C）变换下的对称性。在真空情况下，矩阵形式包括四个实$4 \times 4$矩阵$α^{b}$。在有介质的情况下，矩阵形式需要两组$4 \times 4$矩阵，即$α^{b}$和$β^{b}$，并给出了它们的简单对称实现.在旋量基中找到了$α^{b}$和$β^{b}$与Dirac矩阵的关系，利用SO（3.C）群中的复数3-向量场和复数正交旋转，以简短的代数形式给出了任意线性介质的Minkowski本构关系.研究和讨论了基于两个电磁4矢量$e^α(x) = u_β F^{αβ}(x), b^α (x) = u_β \tilde{F}^{αβ}(x) $的Esposito形式的矩阵复形公式。它被认为是通过使用一个平凡的身份$I=U^{-1}(u)U(u)$的麦克斯韦方程的Esposito形式。
英文摘要：
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation under transformations of the complex rotation group SO(3.C) is demonstrated explicitly. In vacuum case, the matrix form includes four real $4 \times 4$ matrices $α^{b}$. In presence of media matrix form requires two sets of $4 \times 4$ matrices, $α^{b}$ and $β^{b}$ -- simple and symmetrical realization of which is given. Relation of $α^{b}$ and $β^{b}$ to the Dirac matrices in spinor basis is found. Minkowski constitutive relations in case of any linear media are given in a short algebraic form based on the use of complex 3-vector fields and complex orthogonal rotations from SO(3.C) group. The matrix complex formulation in the Esposito's form,based on the use of two electromagnetic 4-vectors, $e^α(x) = u_β F^{αβ}(x), b^α (x) = u_β \tilde{F}^{αβ}(x) $ is studied and discussed. It is argued that Esposito form is achieved trough the use of a trivial identity $I=U^{-1}(u)U(u)$ in the Maxwell equation.
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。
