Tutorial: Macroscopic QED and vacuum forces

TL;DR

This tutorial explains macroscopic QED, a framework for understanding electromagnetic interactions with materials, and demonstrates its application to quantum vacuum forces like quantum friction between moving plates.

Contribution

It develops the macroscopic QED theory from one-dimensional to three-dimensional cases and extends it to moving materials, enabling calculation of quantum electromagnetic forces.

Findings

Reproduces Pendry's quantum friction expression

Extends macroscopic QED to moving dispersive materials

Provides a comprehensive tutorial on macroscopic QED theory

Abstract

This tutorial introduces the theory of macroscopic QED, where a Hamiltonian is found that represents the electromagnetic field interacting with a dispersive, dissipative material. Using a one dimensional theory as motivation, we build up the more cumbersome three dimensional theory. Then considering the extension of this theory to moving materials, where the material response changes due to both the Doppler effect and the mixing of electric and magnetic responses, it is shown that one gets the theory of quantum electromagnetic forces for free. We finish by applying macroscopic QED to reproduce Pendry's expression for the quantum friction force between sliding plates.