物理学方程的射流表述  

Formulation of Jet in Physics Equations

作　　者：宋梓豪 Song Zihao(College of Physical Science and Technology,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学物理科学与技术学院

出　　处：《甘肃科学学报》2019年第6期12-15,共4页Journal of Gansu Sciences

摘　　要：纤维丛工具在杨-米尔斯理论之后被物理学家广泛接受使用,而射流丛是纤维丛中的一个分类别,可以用于直接描述微分方程以及方程组的目的,通过将射流流形的子流形作为微分方程,将构建射流流形的纤维丛上的截面作为微分方程的解的方法,于是可以得到将代数问题转换为流形上的几何问题的结果。对于复杂的微分方程组,还能转换为切触形式来构造微分理想。此外还可以构建约束变分问题,再通过离散等效、勒帕吉等效等方法得到将变分问题大幅度简化的结果,因此得出通过这些方法,物理学微分方程组的计算也能简化的结论。The fiber bundle tool was widely accepted and used by physicians after the Yang-MillsTheory, and jet bundle is one of the categories of fiber bundle. The jet bundle can be used to directly describe the differential equation and the purpose of equation group, by considering the submanifold of jet manifold as the differential equation, the profile on fiber bundle shaping jet manifold as the solution to the differential equation, so as to produce solution to geometry problem in terms of manifold transformed from algebra problem. The complicated differential equation group can be transformed into osculatory form to establish the differential ideal. In addition, the constraint variational problem can also be built and be simplified to a great extent by means of discrete equivalent and Lepage equivalent, which can lead to the conclusion that the calculation of differential equation group in physics can also be simplified by all these means.

关 键 词：数学物理方法 射流丛 外微分系统 理论力学 微分方程 

分 类 号：O411.1[理学—理论物理]