Electromagnetic field fluctuations near a dielectric-vacuum boundary and surface divergences in the ideal conductor limit

TL;DR

This paper investigates electromagnetic field fluctuations near a dielectric-vacuum boundary, analyzing surface divergences in the ideal conductor limit and their implications for Casimir-Polder interactions.

Contribution

It introduces a limiting procedure to study surface divergences of field fluctuations at dielectric-vacuum interfaces approaching ideal conductors.

Findings

Surface divergences occur at the interface in the ideal conductor limit.

The limiting procedure clarifies the structure of these divergences.

Field fluctuations near the surface influence Casimir-Polder interactions.

Abstract

We consider the electric and magnetic field fluctuations in the vacuum state in the region external to a half-space filled with a homogeneous non-dissipative dielectric. We discuss an appropriate limit to an ideal metal and concentrate our interest on the renormalized field fluctuations, or equivalently to renormalized electric and magnetic energy densities, in the proximity of the dielectric-vacuum interface. We show that surface divergences of field fluctuations arise at the interface in an appropriate ideal conductor limit, and that our limiting procedure allows to discuss in detail their structure. Field fluctuations close to the surface can be investigated through the retarded Casimir-Polder interaction with an appropriate polarizable body.