八元数空间中含复合算符的若干场方程
Some field equations with composite operators in octonion spaces
AI总结：
该研究在八元数空间框架下，探究由场强、场势等物理量与四元数算符结合形成的复合算符对引力与电磁场方程的影响，推导得出多种新型场方程，深化了对场方程物理性质的认知。
摘要：
本文旨在探究包含若干物理量的复合算符对引力场与电磁场的影响，研究八元数场方程的影响因素与物理性质。J. C. Maxwell 首次利用四元数与矢量术语描述电磁场。八元数可同时描述电磁场与引力场的物理量，包括八元数场势、场强、场源、线动量、角动量、力矩与力。在八元数空间中，场强与四元数算符可结合为一个复合算符，对场方程具有重要作用。类似地，场势也可与四元数算符构成若干复合算符，且它们会对场方程产生一定影响。此外，其他物理量也可与四元数算符结合形成多种复合算符。在这些复合算符中，多个物理量也会对场方程产生一定影响。换言之，与这些复合算符中的其他物理量相比，场强并不占据唯一的核心地位。在八元数描述的场论中，应用不同的复合算符可推导出各种场方程。根据不同的复合算符，既能推导出场强或/和场势发挥一定作用时的场方程，也能推导出其余物理量发挥一定作用时的若干新场方程，这进一步深化了对场方程物理性质的理解。
英文摘要：
The paper aims to explore the impact of composite operators containing a few physical quantities on the gravitational and electromagnetic fields, studying the influencing factors and physical properties of octonion field equations. J. C. Maxwell first utilized the quaternions and vector terminology to describe the electromagnetic fields. The octonions can be used to simultaneously describe the physical quantities of electromagnetic and gravitational fields, including the octonion field potential, field strength, field source, linear momentum, angular momentum, torque and force. In the octonion spaces, the field strength and quaternion operator are able to combine together to become one composite operator, making an important contribution to the field equations. Similarly, the field potential can also form some composite operators with the quaternion operator, and they have a certain impact on the field equations. Furthermore, other physical quantities can also be combined with the quaternion operator to form several composite operators. In these composite operators, multiple physical quantities can also have a certain impact on the field equations. In other words, the field strength does not occupy a unique central position, compared to other physical quantities in these composite operators. In the field theories described by the octonions, various field equations can be derived from the application of different composite operators. According to different composite operators, it is able to infer the field equations when the field strength or/and field potential make a certain contribution, and it is also possible to deduce several new field equations when the remaining physical quantities play a certain role. This further deepens the understanding of the physical properties of field equations.
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。
