论文标题
重力理论中运动问题
The problem of motion in gauge theories of gravity
论文作者
论文摘要
在本文中，我们考虑了产生重力场的量规负载物质运动的问题，并且由于引力场方程的兼容条件，在仪表场上叠加了哪些方程。从该理论的观点对称性分析了所考虑的问题，就普遍的仪表变形群体而没有规格的拉格朗日人。 特别是表明，沿Riemannian空间的大地测量学的未充电颗粒的运动固有在极为广泛的重力理论中，这是这些理论在满足重力场方程的条件下的量规翻译不变性的结果。由于量规载体的颗粒的原因，概括为仪表载体物质的洛伦兹力在运动方程式出现在运动方程中，这是由于该理论在满足引力和仪表场方程的条件下的量规对称性。此外，我们发现了某些字段方程关系的关系，这些磁场是从关于实现其他字段方程的假设之后的，例如，引力场方程的关系和内部对称性的仪表字段，这是从关于实现物质场方程的假设之后遵循的。特别是，我们获得了在任意仪表场（以及量规征收物质的存在）中概括的身份，希尔伯特（Hilbert）对电磁场发现的身份。 在本文的末尾有一个附录，该附录简要描述了广义规模变形群体理论的主要规定和事实，并提出了对外部（时空）和内部对称性仪表字段的单个组理论解释的主要思想，这是其几何解释的另一种。
In this article we consider the problem to what extent the motion of gauge-charged matter that generates the gravitational field can be arbitrary, as well as what equations are superimposed on the gauge field due to conditions of compatibility of gravitational field equations. Considered problem is analyzed from the point of view symmetry of the theory with respect to the generalized gauge deformed groups without specification of Lagrangians. In particular it is shown, that the motion of uncharged particles along geodesics of Riemannian space is inherent in an extremely wide range of theories of gravity and is a consequence of the gauge translational invariance of these theories under the condition of fulfilling equations of gravitational field. In the cause of gauge-charged particles, the Lorentz force, generalized for gauge-charged matter, appears in equations of motion as a consequence of the gauge symmetry of the theory under the condition of fulfilling equations of gravitational and gauge fields. In addition, we found relationships of equations for some fields that follow from the assumption about fulfilling of equations for other fields, for example, relationships of equations of the gravitational field and the gauge field of internal symmetry which follow from the assumption about fulfilling of equations of matter fields. In particular, we obtained the identity that generalizes in the case of arbitrary gauge field (and in the presence of gauge-charged matter) the identity found by Hilbert for the electromagnetic field. At the end of the article there is an Appendix, which briefly describes the main provisions and facts from the theory of generalized gauge deformed groups and presents the main ideas of a single group-theoretical interpretation of gauge fields of both external (space-time) and internal symmetry, which is an alternative to their geometric interpretation.
