标题： 自旋在任意引力场中 显示英文标题

标题： Spin in an arbitrary gravitational field

摘要： 我们研究在弯曲时空流形上的狄拉克费米子的量子力学。 时空的度规是完全任意的，允许讨论所有可能的惯性及引力场配置。 在此框架中，我们找到了任意经典外部场（包括引力和电磁场）下的厄米狄拉克哈密顿量。 为了讨论量子力学模型的物理内容，我们进一步应用了福尔迪-沃斯胡伊斯恩变换，并推导了自旋和位置算符的量子运动方程。 我们分析了这些方程的半经典极限，并将结果与标准马西森-帕帕佩特鲁理论和经典正则理论框架下带有自旋的经典粒子的动力学进行比较。 在任意引力场中，自旋粒子的量子力学和经典运动方程的比较显示它们完全一致。 显示英文摘要

摘要： We study the quantum mechanics of a Dirac fermion on a curved spacetime manifold. The metric of the spacetime is completely arbitrary, allowing for the discussion of all possible inertial and gravitational field configurations. In this framework, we find the Hermitian Dirac Hamiltonian for an arbitrary classical external field (including the gravitational and electromagnetic ones). In order to discuss the physical content of the quantum-mechanical model, we further apply the Foldy-Wouthuysen transformation, and derive the quantum equations of motion for the spin and position operators. We analyse the semiclassical limit of these equations and compare the results with the dynamics of a classical particle with spin in the framework of the standard Mathisson-Papapetrou theory and in the classical canonical theory. The comparison of the quantum mechanical and classical equations of motion of a spinning particle in an arbitrary gravitational field shows their complete agreement.