Electrodynamic Casimir Effect in a Medium-Filled Wedge II

TL;DR

This paper calculates the Casimir energy in a magnetodielectric wedge with a conducting arc, revealing finite results that avoid divergences typical in idealized geometries, and clarifies the physical implications of boundary assumptions.

Contribution

It provides an explicit expression for the Casimir energy in a wedge geometry with realistic boundary conditions, extending previous idealized models.

Findings

Finite Casimir energy obtained for the wedge with a conducting arc.

Divergences in previous models are attributed to idealized boundary assumptions.

The geometry avoids divergences associated with sharp corners in ideal conductor models.

Abstract

We consider the Casimir energy in a geometry of an infinite magnetodielectric wedge closed by a circularly cylindrical, perfectly conducting arc embedded in another magnetodielectric medium, under the condition that the speed of light be the same in both media. An expression for the Casimir energy corresponding to the arc is obtained and it is found that in the limit where the reflectivity of the wedge boundaries tends to unity the finite part of the Casimir energy of a perfectly conducting wedge-shaped sheet closed by a circular cylinder is regained. The energy of the latter geometry possesses divergences due to the presence of sharp corners. We argue how this is a pathology of the assumption of ideal conductor boundaries, and that no analogous term enters in the present geometry.