QED vacuum between an unusual pair of plates

TL;DR

This paper analyzes the quantum electromagnetic vacuum between a perfectly conducting and an infinitely permeable plate, deriving explicit field correlators, revisiting the Casimir effect, and discussing the Scharnhorst light velocity shift in this setup.

Contribution

It provides explicit expressions for vacuum field correlators in a novel plate configuration, enabling analysis of Casimir and Scharnhorst effects in this context.

Findings

Reobtained the Casimir effect for the mixed boundary conditions.

Derived explicit vacuum expectation values of electric and magnetic field operators.

Discussed the implications for light velocity shifts (Scharnhorst effect) in this configuration.

Abstract

We consider the photon field between an unusual configuration of infinite parallel plates: a perfectly conducting plate $(\epsilon\to\infty)$ and an infinitely permeable one $\mu\to\infty)$. After quantizing the vector potential in the Coulomb gauge, we obtain explicit expressions for the vacuum expectation values of field operators of the form $<{\hat E}_i{\hat E}_j>_0$ and $<{\hat B}_i{\hat B}_j>_0$. These field correlators allow us to reobtain the Casimir effect for this set up and to discuss the light velocity shift caused by the presence of plates (Scharnhorst effect \cite{Scharnhorst,Barton,BarScharn}) for both scalar and spinor QED.