物质介质中矢量星等的守恒量
Conserved quantities of vectorial magnitudes within the material media
摘要：
利用八元数坐标系的旋转变换，探讨了物质介质中与矢量幅度有关的守恒量的物理性质，揭示了电磁场和引力场中某些守恒量的不变性。J. C.麦克斯韦首先利用四元数的代数来描述电磁理论。随后的学者同时研究了电磁场和引力场的物理性质，包括物质介质内的八元数线动量、角动量、力矩和力。根据八元数代数，在八元数坐标系的旋转变换中，八元数物理量的标量部分保持不变，而矢量部分可能发生变化。从八元数的特征出发，推导出八元数空间$\mathbb{O}$中与矢量量有关的守恒量，包括线动量、角动量、力矩和力的量。同样，它也能推导出变换后的八元数空间$\mathbb{O}_u$中与矢量大小有关的几个守恒量，包括电流、磁矩和电矩的大小。通过分析和比较，得出结论：从八元数空间的观点来看，一些与矢量量有关的守恒量是不能同时成立的。这有助于加深对与矢量幅度有关的某些守恒量的进一步理解。
英文摘要：
By means of the rotational transformations of octonion coordinate systems, the paper aims to explore the physical properties of conserved quantities relevant to the vectorial magnitudes within the material media, revealing the simultaneity of some conserved quantities in the electromagnetic and gravitational fields. J. C. Maxwell first utilized the algebra of quaternions to describe the electromagnetic theory. The subsequent scholars studied the physical properties of electromagnetic and gravitational fields simultaneously, including the octonion linear momentum, angular momentum, torque and force within the material media. According to the algebra of octonions, the scalar parts of octonion physical quantities remain unchanged, while the vectorial parts may alter, in the rotational transformations of octonion coordinate systems. From the octonion characteristics, it is able to deduce a few conserved quantities related to the vectorial magnitudes in the octonion space $\mathbb{O}$, including the magnitudes of linear momentum, angular momentum, torque and force. Similarly, it is capable of inferring several conserved quantities relevant to the vectorial magnitudes in the transformed octonion space $\mathbb{O}_u$, including the magnitudes of electric current, magnetic moment and electric moment. Through the analysis and comparison, it is concluded that some conserved quantities, relevant to the vectorial magnitudes, are unable to be established simultaneously, from the point of view of the octonion spaces. This is helpful to deepen the further understanding of some conserved quantities related to the vectorial magnitudes.
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