Scalar QED $\hbar$-Corrections to the Coulomb Potential

TL;DR

This paper calculates the one-loop quantum corrections to the Coulomb potential in scalar QED, ensuring gauge independence, and highlights gaps in previous quantum gravity studies, serving as a step towards similar analyses in quantum gravity.

Contribution

It provides the first detailed derivation of gauge-independent 1-loop corrections to the Coulomb potential in scalar QED from scattering amplitudes.

Findings

Derived gauge-invariant quantum corrections to Coulomb potential

Identified incompleteness in prior quantum gravity studies

Established a framework for future quantum gravity corrections

Abstract

The leading long-distance 1-loop quantum corrections to the Coulomb potential are derived for scalar QED and their gauge-independence is explicitly checked. The potential is obtained from the direct calculation of the 2-particle scattering amplitude, taking into account all relevant 1-loop diagrams. Our investigation should be regarded as a first step towards the same programme for effective Quantum Gravity. In particular, with our calculation in the framework of scalar QED, we are able to demonstrate the incompleteness of some previous studies concerning the Quantum Gravity counterpart.