赝矢量的几何本质  

The Geometric Nature of Pseudovector

作　　者：刘畅[1] 牛奔 孙钰韬 刘世兴[1] LIU Chang;NIU Ben;SUN Yu-tao;LIU Shi-xing(School of Physics,Liaoning University,Shenyang 110036,China)

机构地区：[1]辽宁大学物理学院,辽宁沈阳110036

出　　处：《辽宁大学学报（自然科学版）》2024年第3期200-207,共8页Journal of Liaoning University：Natural Sciences Edition

基　　金：国家自然科学基金(12372002);辽宁省教育厅科学技术研究一般项目(LJKZ0089);辽宁大学本科教学改革项目(JG2021KCSZ013);辽宁大学2023年研究生优质课程建设与教学模式综合改革研究项目(YJG202302097)。

摘　　要：本文借助于微分几何中的外积运算、微分形式、Hodge星算子等基本概念,探究了赝矢量的几何本质是微分2-形式,又借助Hodge星算子,给予微分2-形式可以被称为赝矢量的合理解释.通过将叉积运算替换为外积运算,清晰地解释了赝矢量、真矢量及其混合运算规则的逻辑关系,举例说明赝矢量及其运算在力学和电动力学等领域中的应用.特别是,应用赝矢量的运算规则给出了向心加速度是真矢量的合理解释.With the help of the basic notions in differential geometry,such as wedge product,differential form and Hodge star-operator,we explored the geometric nature of the pseudovector is a differential 2-form,and give a reasonable explanation that the differential 2-form can be called pseudovector with the help of Hodge star-operator.The logical relations of pseudovector,true vector and their mixed operation rules are clearly explained by replacing the cross product operation with exterior product operation.And the application of pseudovector and its operation in mechanics and electrodynamics is illustrated with examples.Especially,the reasonable logical explanation that the centripetal acceleration is a true vector is given by applying the operation rules of the pseudovector.

关 键 词：真矢量 赝矢量 叉积 外积 

分 类 号：O411[理学—理论物理]