Interesting features of semiclassical gravitational deflection

Abstract

The deflection of any particle by an external weak gravitational field in the framework of Einstein’s general relativity (which is a geometrical theory) is, of course, non-dispersive. Nonetheless, things are completely different if the deflection is studied within the context of semiclassical gravity (or tree-level gravity). Indeed, to first order the cross sections corresponding to the scattering of different quantum particles by a weak gravity field, treated as an external field, as well as the related bending angles, are spin dependent, while to second order the deflection is dispersive (energy dependent). Interestingly enough, in the framework of semiclassical higher-derivative gravity the bending is already energy dependent to first order. In this paper we discuss these disagreements between quantum mechanics and the equivalence principle.