Abstract
The phenomenology of quantum systems in curved space-times is among the most fascinating fields of physics, allowing---often at the gedankenexperiment level---constraints on tentative theories of quantum gravity. Determining the dynamics of fields in curved backgrounds remains, however, a complicated task because of the highly intricate partial differential equations involved, especially when the space metric exhibits no symmetry. In this article, we provide---in a pedagogical way---a general formalism to determine this dynamics at the semiclassical order. To this purpose, a generic expression for the semiclassical propagator is computed and the equation of motion for the probability four-current is derived. Those results underline a direct analogy between the computation of the propagator in general relativistic quantum mechanics and the computation of the propagator for stationary systems in nonrelativistic quantum mechanics. A possible application of this formalism to curvature-induced quantum interferences is also discussed.
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