# Manipulating the Coulomb interaction: A Green's function perspective

## TL;DR

This paper develops a comprehensive Green's function-based framework to analyze Coulomb interactions in complex environments, enabling precise calculations of potentials and forces in media with arbitrary shapes and properties.

## Contribution

It introduces a unified theoretical approach using macroscopic quantum electrodynamics to study Coulomb interactions in diverse environments, including novel geometries.

## Key findings

- Reproduces the screened Coulomb force
- Accounts for local-field effects
- Analyzes interactions in complex geometries such as cavities and plates

## Abstract

We present a unified framework for studying Coulomb interactions in arbitrary environments using macroscopic quantum electrodynamics on the basis of the electromagnetic Green's function. Our theory can be used to derive the Coulomb potential of a single charged particle as well as that between two charges in the presence of media, bodies and interfaces of arbitrary shapes. To demonstrate this, we reproduce the well-known screened Coulomb force, account for local-field effects and consider new cases such as a dielectric cavity and a conducting plate with a hole.