Integral Formulation of Macroscopic Quantum Electrodynamics in Dispersive Dielectric Objects

TL;DR

This paper introduces an integral formulation of macroscopic quantum electrodynamics for dispersive dielectric objects, enabling the use of classical computational methods for quantum problems in complex environments.

Contribution

It presents a novel integral approach using the Hopfield model that connects quantum electrodynamics with classical Green function techniques for dispersive media.

Findings

Allows direct application of classical electrodynamics computational methods to quantum problems.

Provides a framework for quantum electrodynamics in open, dispersive, and absorbing environments.

Facilitates more efficient and accurate quantum simulations in complex dielectric systems.

Abstract

We propose an integral formulation of macroscopic quantum electrodynamics in the Heisenberg picture for linear dispersive dielectric objects of finite size, utilizing the Hopfield-type approach. By expressing the electromagnetic field operators as a function of the polarization density field operator via the retarded Green function for the vacuum, we obtain an integral equation that governs the evolution of the polarization density field operator. This formulation offers significant advantages, as it allows for the direct application of well-established computational techniques from classical electrodynamics to perform quantum electrodynamics computations in open, dispersive, and absorbing environments.