论文标题
曲线时空上狄拉克场的半古典分析
Semiclassical analysis of Dirac fields on curved spacetime
论文作者
论文摘要
我们在任意时空背景和存在固定电磁场的情况下对狄拉克场进行了半经典分析。我们的方法基于Wentzel-Kramers-brillouin近似，并且在小型扩展参数$ \ hbar $中以领先和临近领先顺序分析结果。考虑到波数据包的内部和外部自由度之间的自旋轨道耦合，我们以自旋依赖性项得出有效的射线方程。这些方程式描述了局部狄拉克波包的重力自旋效应。我们对巨大和无质量的迪拉克场进行处理，并显示协变量定义的浆果连接以及相关的浆果曲率如何控制半经典动力学。重力自旋霍尔方程被证明是用于旋转对象的Mathisson-Papapetrou方程的特殊情况。
We present a semiclassical analysis for Dirac fields on an arbitrary spacetime background and in the presence of a fixed electromagnetic field. Our approach is based on a Wentzel-Kramers-Brillouin approximation, and the results are analyzed at leading and next-to-leading order in the small expansion parameter $\hbar$. Taking into account the spin-orbit coupling between the internal and external degrees of freedom of wave packets, we derive effective ray equations with spin-dependent terms. These equations describe the gravitational spin Hall effect of localized Dirac wave packets. We treat both massive and massless Dirac fields and show how a covariantly defined Berry connection and the associated Berry curvature govern the semiclassical dynamics. The gravitational spin Hall equations are shown to be particular cases of the Mathisson-Papapetrou equations for spinning objects.
