论文标题
关于与自旋的颗粒自由运动的保守量
On Conserved Quantities for the Free Motion of Particles with Spin
论文作者
论文摘要
在80年代初期，R.Rüdiger发表了一对文章，其中发现与粒子在弯曲时空中移动的颗粒运动相关的最一般的保守性电荷。特别是，除了与杀死向量相关的众所周知的保守量外，如果时空接收杀伤YANO张量，则还可以具有另一个在粒子自旋中线性的保守量。但是，在这些论文中，证明为了使这一新标量保留两个晦涩的条件，涉及杀戮量张量和曲率必须遵守。在本文中，我们试图阐明这些条件，并最终证明这种保守数量对于大多数物理相关的空间是没有用的。值得注意的是，对于在真空中移动的颗粒（Einstein Pacetighter），使用杀伤量张量构建的保守标量将无助于整合运动方程。此外，我们证明，由于这些晦涩的条件，杀戮Yano张量必须是协变量的。
In the early 80's, R. Rüdiger published a pair of articles in which it was found the most general conserved charges associated to the motion of particles with spin moving in curved spacetime. In particular, it was shown that besides the well-known conserved quantity associated to Killing vectors, it is also possible to have another conserved quantity that is linear in the spin of the particle if the spacetime admits a Killing-Yano tensor. However, in these papers it was proved that in order for this new scalar to be conserved two obscure conditions involving the Killing-Yano tensor and the curvature must be obeyed. In the present paper we try to shed light over these conditions and end up proving that this conserved quantity is useless for most physically relevant spacetimes. Notably, for particles moving in vacuum (Einstein spacetimes) this conserved scalar constructed with the Killing-Yano tensor will not help on the integration of the equations of motion. Moreover, we prove that, as a consequence of these obscure conditions, the Killing-Yano tensor must be covariantly constant.
