Semiclassical and Effective Theories of Gravitation

TL;DR

This paper calculates first and second order corrections for particle scattering in a weak gravitational field, revealing spin and energy-dependent violations of the Equivalence Principle, and connects these results to Effective Theory of Gravitation.

Contribution

It demonstrates that quantum corrections lead to violations of the Equivalence Principle and links these findings to the Effective Theory of Gravitation in specific limits.

Findings

Cross-sections depend on spin at first order.

Higher-order corrections depend on energy.

Potential to set bounds on photon mass and detect Equivalence Principle violations.

Abstract

First and second order corrections for the scattering of different types of particles by a weak gravitational field, treated as an external field, are calculated. These computations indicate a violation of the Equivalence Principle: to first order, the cross-sections are spin dependent; if the calculations are pushed to the next order, they become dependent upon energy as well. Interesting enough, the aforementioned results are equivalent to those obtained by means of the so-called Effective Theory of Gravitation, in the limit in which one of the masses is much greater than all the other energies involved. We discuss also some applications of our research, such as the determination of an upper bound for the photon mass, and the possible detection, in the foreseeable future, of these violations of the Equivalence Principle.