Trajectory of a massive localized wave function in a curved spacetime geometry

Propagation of a localized wave function of a massive scalar field is investigated in its rest frame. The complete orthogonal Hermite-Gauss basis is presented, and the Gouy phase and Rayleigh scale notions are adapted. The leading and subleading gravitational corrections to a localized quantum wave function propagating in a generally curved spacetime geometry are calculated within the Fermi coordinates around the timelike geodesic of its rest frame, and cross-talk coefficients among the modes are derived. It is observed that spherically symmetric modes propagate along the geodesic. However, nonspherical modes are found to experience a mode-dependent residual quantum force at the subleading order. It is shown that the residual force does not generate an escape velocity for in-falling wave functions but leads to a mode-dependent deflection angle for the scattered ones.

Automated summary

This paper investigates the propagation of a localized wave function of a massive scalar field in its rest frame. It presents the complete orthogonal Hermite-Gauss basis and adapts the Gouy phase and Rayleigh scale notions. The paper calculates the leading and subleading gravitational corrections to a localized quantum wave function propagating in a generally curved spacetime geometry and derives cross-talk coefficients among the modes. The study shows that spherically symmetric modes propagate along the geodesic, while nonspherical modes experience a mode-dependent residual quantum force at the subleading order.