Field theoretic description of partially reflective surfaces

TL;DR

This paper develops a field theoretic model for electromagnetic interactions with partially reflective surfaces, deriving an exact photon propagator that interpolates between transparent and perfect mirror limits.

Contribution

It introduces an enlarged Maxwell Lagrangian and computes an exact photon propagator for semitransparent surfaces, extending the understanding of charge-surface interactions.

Findings

Exact photon propagator for partially reflective surfaces

Reduction to perfect conductor case in the limit

Interaction model interpolates transparency levels

Abstract

The issue of electric charges in interaction with partially reflective surfaces is addressed by means of field theoretic methods. It is proposed an enlarged Maxwell lagrangian, describing the electromagnetic field in the presence of a semitransparent surface, and its corresponding photon propagator is computed exactly. The amended Green function reduces to the one for a perfect conductor in the appropriate limit, and leads to the interaction between charges and surfaces with varying degrees of transparency, featured by a phenomenological parameter. The interaction found via image method is recovered, in the limiting case of perfect mirrors, as a testimony to the validity of the model.