时空曲率对自旋1/2粒子Zitterbewegung的影响
Effects of Space-Time Curvature on Spin-1/2 Particle Zitterbewegung
摘要：
本文研究了自旋1/2粒子Zitterbewegung在一般弯曲时空背景下的性质，该背景用费米正规坐标描述，其中空间部分用一般曲线坐标表示。采用Barut和Bracken首先介绍的方法Zitterbewegung在局部静止框架的粒子，它表明，非平凡的引力的相对位置和动量算符的贡献出现由于耦合的Zitterbewegung频率项与Ricci曲率张量在费米框架，表明形式上违反弱等效原理。这些贡献的显式表达式示出的情况下，准圆轨道运动的自旋1/2粒子在Vaidya背景。由于时空曲率效应与Zitterbewegung频率的耦合，Pauli-Lubanski矢量的时间导数也出现了正式的表达式。此外，曲线坐标的选择导致自旋为1/2的粒子的正则动量的时间演化中的非惯性贡献，其中Zitterbewegung效应导致其传播的稳定性考虑，基于Floquet微分方程理论。
英文摘要：
This paper investigates the properties of spin-1/2 particle Zitterbewegung in the presence of a general curved space-time background described in terms of Fermi normal co-ordinates, where the spatial part is expressed using general curvilinear co-ordinates. Adopting the approach first introduced by Barut and Bracken for Zitterbewegung in the local rest frame of the particle, it is shown that non-trivial gravitational contributions to the relative position and momentum operators appear due to the coupling of Zitterbewegung frequency terms with the Ricci curvature tensor in the Fermi frame, indicating a formal violation of the weak equivalence principle. Explicit expressions for these contributions are shown for the case of quasi-circular orbital motion of a spin-1/2 particle in a Vaidya background. Formal expressions also appear for the time-derivative of the Pauli-Lubanski vector due to space-time curvature effects coupled to the Zitterbewegung frequency. As well, the choice of curvilinear co-ordinates results in non-inertial contributions in the time evolution of the canonical momentum for the spin-1/2 particle, where Zitterbewegung effects lead to stability considerations for its propagation, based on the Floquet theory of differential equations.
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