Effective Field Theory of Gravity: Leading Quantum Gravitational Corrections to Newtons and Coulombs Law

TL;DR

This paper uses effective field theory to compute quantum corrections to Newton's and Coulomb's laws, revealing both classical post-Newtonian and genuine quantum effects at low energies.

Contribution

It provides a detailed calculation of one-loop quantum corrections to gravity and electromagnetism within an effective field theory framework, including derivation of Feynman rules and scattering amplitudes.

Findings

Derivation of post-Newtonian corrections of order Gm/c^2 r

Calculation of genuine quantum corrections of order Għ/c^3 r^2

Explicit form of quantum corrections to Newton and Coulomb potentials

Abstract

In this paper we consider general relativity and its combination with scalar quantum electrodynamics (QED) as an effective quantum field theory at energies well below the Planck scale. This enables us to compute the one-loop quantum corrections to the Newton and Coulomb potential induced by the combination of graviton and photon fluctuations. We derive the relevant Feynman rules and compute the nonanalytical contributions to the one-loop scattering matrix for charged scalars in the nonrelativistic limit. In particular, we derive the post-Newtonian corrections of order $Gm/\text c^2 r$ from general relativity and the genuine quantum corrections of order $G\hbar/\text c^3 r^2$.