We extend the biquaternionic Dirac equation to include interactions with a background bosonic Geld. The obtained biquaternionic Dirac equation yields Maxwell-like equations that hold for both a matter Geld and an electromagnetic Geld. We establish that the electric Geld is perpendicular to the matter magnetic Geld and the magnetic Geld is perpendicular to the matter inertial Geld. We show that the inertial and magnetic masses are conserved separately. The magnetic mass density arises as a result of the coupling between the vector potential and the matter inertial Geld. The presence of the vector and scalar potentials and also the matter inertial and magnetic Gelds modify the Standard form of the derived Maxwell equations. The resulting interacting electrodynamics equations are generalizations of the equations of Wilczek or Chern-Simons axion-like Gelds. The coupled Geld in the biquaternioic Dirac Geld reconstructs the Wilczek axion Geld. We show that the electromagnetic Geld vector $$\overrightarrow{F}=\overrightarrow{E}+ic\overrightarrow{B}$$ F → = E → + i c B → , where $$\overrightarrow{E}$$ E → and $$\overrightarrow{B}$$ B → are the respective electric and magnetic Gelds, satisGes the massive Dirac equation and, moreover, $$\overrightarrow{\triangledown}\cdot\overrightarrow{F}=0$$ ▽ → ⋅ F → = 0 .

中文翻译：

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双四元狄拉克场与玻色场的耦合

我们扩展了双四元数狄拉克方程，以包括与背景玻色格尔德的相互作用。获得的双四元数狄拉克方程产生了类麦克斯韦方程，适用于物质 Geld 和电磁 Geld。我们确定电凝胶垂直于物质磁凝胶，磁凝胶垂直于物质惯性凝胶。我们表明惯性质量和磁质量是分开守恒的。磁质量密度的产生是矢量势与物质惯性 Geld 之间耦合的结果。矢量和标量势以及物质惯性和磁性 Geld 的存在修改了导出的麦克斯韦方程的标准形式。由此产生的相互作用的电动力学方程是 Wilczek 或 Chern-Simons 轴子状 Gelds 方程的推广。双季铵盐 Dirac Geld 中的耦合 Geld 重建了 Wilczek 轴子 Geld。我们证明了电磁 Geld 向量 $$\overrightarrow{F}=\overrightarrow{E}+ic\overrightarrow{B}$$ F → = E → + ic B → ，其中 $$\overrightarrow{E}$$ E → 和 $$\overrightarrow{B}$$ B → 分别是电和磁的 Geld，满足大规模狄拉克方程，而且，$$\overrightarrow{\triangledown}\cdot\overrightarrow{F}=0$$ ▽ → ⋅ F → = 0 。