论文标题
弯曲空间中局部量子粒子的波函数描述
A Wavefunction Description for a Localized Quantum Particle in Curved Spacetimes
论文作者
论文摘要
我们将旋转1/2粒子的旋转纺纱形式降低到弯曲空间中的复杂波函数描述。我们在弯曲的空间中考虑了局部的费米粒子，并在系统质量中心周围的加速度和曲率方面进行膨胀，从而推广[Phys的结果。 Rev. D 22，1922年]。在非权利主义近似值下，一个人在系统的休息空间中定义的复杂波形的希尔伯特空间中获得了量子描述。然后，粒子的波函数根据与对称的哈密顿式相关的修改后的schrödinger方程而演变。与标准schrödinger方程相比，我们的波函数沿其轨迹的质量和曲率的加速度来获得校正。总而言之，我们提供了一种形式主义，用于使用复杂的波功能来描述弯曲的空间中的局部量子粒子。
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 [Phys. Rev. D 22, 1922]. 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 Schrödinger equation associated with a symmetric Hamiltonian. When compared to the standard Schrödinger 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.
