有挠时空理论中质点运动方程研究

The Study on Particle’s Equations of Motion in the Space-Time with Torsion

在有挠时空中推导质点运动方程的过程可归结为下述四步骤:一、写出物理体系的物质场拉氏量和引力场拉氏量;二、计算物质场的能动张量密度;三、写出质点的4维动量,利用狄拉克δ函数的特性,可找到该物质体系物质场的能动张量密度与质点的4维动量的关系;四、考虑拉氏量的对称性和守恒律,以获得物质场的能动张量密度、广义自旋密度和时空曲率、挠率的关系。由此关系即可导出有挠时空中质点运动方程。为了澄清当前一些人对有挠时空中质点运动方程的一些误解,本文将着重讲解上述四步骤的理论基础。本文还将说明,广义相对论中的质点运动方程是有挠引力理论中的质点运动方程的特殊情况,狭义相对论中的质点运动方程是广义相对论中的质点运动方程的特殊情况。

The process of deriving the particle’s equations of motion in the space-time with torsion can be formulated as the following four steps: first, writing the Lagrangian of matter field and gravitational field for the physical system;second, calculating the energy-momentum tensor density of matter field;third, writing the particle’s momentum, and using the Dirac delta function, the relations between energy-momentum tensor density of the matter field and its particle’s momentum can be found;fourth, considering the Lagrangian symmetry and conservation law of the physical system the relations among energy-momentum tensor density and generalized spin density, and space-time curvature, and torsion can be found. From this relation, the equations of motion for the particle in the space-time with torsion can be derived. In order to clarify some people’s misun-derstanding of the equations of motion for particles in space-time with torsion, we mainly explain the theoretical basis of the above four steps in this article. And this paper will also show that the particle’s equations of motion in general relativity are the special case of particle’s equations of motion in torsional gravity, and the particle’s equations of motion in the special relativity are the special case of particle’s equations of motion in general relativity.