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Abstract: The phenomenology of quantum systems in curved space-times is among the mostfascinating fields of physics, allowing -often at the gedankenexperimentlevel- constraints on tentative theories of quantum gravity. Determining thedynamics of fields in curved backgrounds remains however a complicated taskbecause of the highly intricate partial differential equations involved,especially when the space metric exhibits no symmetry. In this article, weprovide -in a pedagogical way- a general formalism to determine this dynamicsat the semiclassical order. To this purpose, a generic expression for thesemiclassical propagator is computed and the equation of motion for theprobability four-current is derived. Those results underline a direct analogybetween the computation of the propagator in general relativistic quantummechanics and the computation of the propagator for stationary systems innon-relativistic quantum mechanics. A possible application of this formalism tocurvature-induced quantum interferences is also discussed.



Author: J. Grain, A. Barrau

Source: https://arxiv.org/







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