Abstract We have found an approximate solution of Dirac equation using Foldy-Wouthuysen-Tani Hamiltonian of a Dirac particle in the Kerr gravitational field. We have solved the equation approximately using time-independent perturbation theory for the positive energy states. We have found frequencies by which these states oscillate. Difference of the periods of any of these two states has an identical form of the classical gravitomagnetic clock effect where the terms are quantized. So that, we have found a quantum version of the gravitomagnetic clock effect of a Dirac fermion in the Kerr gravitational field.

中文翻译：

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克尔引力场中的量子重磁钟效应

摘要 我们利用克尔引力场中狄拉克粒子的Foldy-Wouthuysen-Tani哈密顿量找到了狄拉克方程的近似解。我们已经对正能量状态使用与时间无关的微扰理论近似求解了该方程。我们已经找到了这些状态振荡的频率。这两种状态中任何一种的周期差异具有与经典重磁钟效应相同的形式，其中这些项被量化。因此，我们在克尔引力场中发现了狄​​拉克费米子的引力磁钟效应的量子版本。