Dirac-Kähler场、旋量技术和双电荷电动力学的双势方法
Dirac-Kähler field, spinor technique, and 2-potential approach to electrodynamics with two charges
摘要：
本文从16分量Dirac Kähler场论出发，导出了两种不同宇称的无质量矢量光子场的旋量方程。它们的等效张量方程的强度张量$F_{ab}$和相应的4-矢量$A_{b}$和4-pseudovector $\tilde{A}_{b}$取决于固有光子宇称导出;它们包括额外的源，电4-矢量$j_{b}$和磁4-pseudovector $\tilde{j}_{b}$。两种类型的光子场的理论是明确解耦的，它们通过求和或相减的线性组合导致了在2势方法中具有电荷和磁荷的麦克斯韦电动力学。因此，磁荷的存在性问题可以理解为内禀宇称下不同光子场的超选择定则。整个分析直接扩展到弯曲的时空背景。在扩展的麦克斯韦理论的框架中，已知的电磁二象性被描述为混合了涉及具有不同宇称的光子的场变量的线性变换。扩展的对偶变换涉及强度张量和4-势$A_{b}, \tilde{A}_{b}$。
英文摘要：
From the 16-component Dirac-Kähler field theory, spinor equations for two types of massless vector photon fields with different parities have been derived. Their equivalent tensor equations in terms of the strength tensor $F_{ab}$ and respective 4-vector $A_{b}$ and 4-pseudovector $\tilde{A}_{b}$ depending on intrinsic photon parity are derived; they include additional sources, electric 4-vector $j_{b}$ and magnetic 4-pseudovector $\tilde{j}_{b}$. The theories of two types of photon fields are explicitly uncoupled, their linear combination through summing or subtracting results in Maxwell electrodynamics with electric and magnetic charges in 2-potential approach. So the problem of existence of magnetic charge can be understood as a super selection rule for different photon fields in intrinsic parity. The whole analysis is extended straightforwardly to a curved space-time background. In the frames of that extended Maxwell theory, the known electromagnetic duality is described as a linear transformation mixing the field variables referred to photons with different parities. That extended dual transformation concerns both strength tensors and 4-potentials $A_{b}, \tilde{A}_{b}$.
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