自由光子场方程和类Dirac方程的Lorentz不变Majorana形式
Lorentz Invariant Majorana Formulation of the Field Equations and Dirac-like Equation for the Free Photon
摘要：
本文给出了场方程的一种新的几何形式（Clifford代数形式），它与参考系和所选坐标系无关，它处理的是复1-向量$Ψ=E-icB$（$i$是单位虚数），它是Majorana的复3D量$\mathbfΨ=\mathbf{E}-ic\mathbf{B}$的四维几何推广。当没有源时，复$Ψ$场方程变成自由光子的类狄拉克相对论波动方程。在“基准”观测者（测量场的观测者是静止的）的框架下，在标准基下，四维$Ψ$场方程的分量形式再现了三维$\mathbfΨ$场的麦克斯韦方程组的分量形式.讨论了4D $Ψ$方法和3D $\mathbfΨ$方法的重要区别。
英文摘要：
In this paper we present a new geometric formulation (Clifford algebra formalism) of the field equations, which is independent of the reference frame and of the chosen system of coordinates in it. This formulation deals with the complex 1-vector $Ψ=E-icB$ ($i$ is the unit imaginary), which is four-dimensional (4D) geometric generalization of Majorana's complex 3D quantity $\mathbfΨ=\mathbf{E}-ic\mathbf{B}$. When the sources are absent the field equations with the complex $Ψ$ become Dirac-like relativistic wave equations for the free photon. In the frame of ``fiducial'' observers (the observers who measure fields are at rest) and in the standard basis the component form of the field equations with 4D $Ψ$ reproduces the component form of Majorana-Maxwell equations with 3D field $\mathbfΨ$. The important differences between the approach with the 4D $Ψ$ and that one with the 3D $\mathbfΨ$ are discussed.
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