Casimir densities for wedge-shaped boundaries

TL;DR

This paper calculates vacuum expectation values for scalar and electromagnetic fields in a wedge-shaped region with a cylindrical boundary, revealing attractive vacuum forces induced by the boundary.

Contribution

It provides explicit formulas for vacuum densities in wedge geometries with cylindrical boundaries, including effects of boundary conditions and induced forces.

Findings

Vacuum forces on wedge sides are attractive.

Explicit expressions for vacuum expectation values are derived.

Boundary conditions significantly influence vacuum densities.

Abstract

The vacuum expectation values of the field squared and the energy-momentum tensor are investigated for a scalar field with Dirichlet boundary conditions and for the electromagnetic field inside a wedge with a coaxial cylindrical boundary. In the case of the electromagnetic field perfectly conducting boundary conditions are assumed on the bounding surfaces. By using the Abel-Plana-type formula for the series over the zeros of the Bessel function, the vacuum expectation values are presented in the form of the sum of two terms. The first one corresponds to the geometry without a cylindrical boundary and the second one is induced by the presence of the cylindrical shell. The additional vacuum forces acting on the wedge sides due the presence of the cylindrical boundary are evaluated and it is shown that these forces are attractive for both scalar and electromagnetic fields.