Canonical quantization of electromagnetism in spatially dispersive media

TL;DR

This paper develops a quantum theory of electromagnetism in spatially dispersive media, showing that nonlocal responses naturally regularize divergences and impact Casimir effect calculations.

Contribution

It introduces a quantized electromagnetic action in spatially dispersive media and demonstrates automatic regularization of divergences due to nonlocal responses.

Findings

Nonlocal response regularizes electromagnetic divergences.

Finite electromagnetic field intensity at fixed frequency.

Implications for Casimir effect calculations.

Abstract

We find the action that describes the electromagnetic field in a spatially dispersive, homogeneous medium. This theory is quantized and the Hamiltonian is diagonalized in terms of a continuum of normal modes. It is found that the introduction of nonlocal response in the medium automatically regulates some previously divergent results, and we calculate a finite value for the intensity of the electromagnetic field at a fixed frequency within a homogeneous medium. To conclude we discuss the potential importance of spatial dispersion in taming the divergences that arise in calculations of Casimir-type effects.