We reduce Dirac’s spinor formalism for a spin 1/2 particle to a complex wavefunction description in curved spacetimes. We consider a localized fermionic particle in curved spacetimes and perform an expansion in terms of the acceleration and curvature around the center of mass of the system, generalizing the results of Parker (1980 Phys. Rev. Lett. 44 1559), Parker (1980 Phys. Rev. D 22 1922–1934). Under a non-relativistic approximation, one obtains a quantum description in a Hilbert space of complex wavefunctions defined in the rest space of the system. The wavefunction of the particle then evolves according to a modified Schrdinger equation associated with a symmetric Hamiltonian. When compared to the standard Schrdinger equation for a wavefunction, we obtain corrections in terms of the acceleration of the system’s center of mass and curvature of spacetime along its trajectory. In summary, we provide a formalism for the use of a complex wavefunction to describe a localized quantum particle in curved spacetimes.

我们将自旋 1/2 粒子的狄拉克旋量形式化简化为弯曲时空中的复杂波函数描述。我们考虑弯曲时空中的局部费米子粒子，并根据系统质心周围的加速度和曲率进行扩展，概括了 Parker (1980 Phys. Rev. Lett. 44 1559)、Parker (1980 Phys . 修订版D 221922-1934 年）。在非相对论近似下，可以在系统的其余空间中定义的复波函数的希尔伯特空间中获得量子描述。然后，粒子的波函数根据与对称哈密顿量相关的修正 Schrdinger 方程演化。与波函数的标准薛定谔方程相比，我们获得了系统质心加速度和沿其轨迹的时空曲率的修正。总之，我们提供了使用复波函数来描述弯曲时空中的局域量子粒子的形式。