Leading quantum gravitational corrections to QED

TL;DR

This paper calculates the leading quantum and post-Newtonian corrections to the scattering amplitude of charged fermions in a combined quantum gravity and QED framework, providing insights into long-range quantum effects.

Contribution

It introduces a method to compute the leading quantum gravitational corrections to QED interactions using an effective field theory approach.

Findings

Derived the non-analytical parts of the 1-loop scattering amplitude.

Constructed the leading quantum-corrected potential for charged fermions.

Provided a framework for combining quantum gravity and QED corrections.

Abstract

We consider the leading post-Newtonian and quantum corrections to the non-relativistic scattering amplitude of charged spin-1/2 fermions in the combined theory of general relativity and QED. The coupled Dirac-Einstein system is treated as an effective field theory. This allows for a consistent quantization of the gravitational field. The appropriate vertex rules are extracted from the action, and the non-analytic contributions to the 1-loop scattering matrix are calculated in the non-relativistic limit. The non-analytical parts of the scattering amplitude are known to give the long range, low energy, leading quantum corrections, are used to construct the leading post-Newtonian and quantum corrections to the two-particle non-relativistic scattering matrix potential for two massive fermions with electric charge.