Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries

TL;DR

This paper calculates the vacuum expectation values of the Wightman function, field square, and energy-momentum tensor for a massive scalar field inside a wedge with two cylindrical boundaries, revealing attractive interaction forces.

Contribution

It introduces a method using the generalized Abel-Plana formula to separate single-shell and interference contributions for scalar fields with Dirichlet boundary conditions.

Findings

Interaction forces between boundaries are always attractive.

Explicit expressions for vacuum densities are derived in various asymptotic regions.

The approach can be extended to Neumann boundary conditions.

Abstract

Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with general curvature coupling parameter inside a wedge with two coaxial cylindrical boundaries. It is assumed that the field obeys Dirichlet boundary condition on bounding surfaces. The application of a variant of the generalized Abel-Plana formula enables to extract from the expectation values the contribution corresponding to the geometry of a wedge with a single shell and to present the interference part in terms of exponentially convergent integrals. The local properties of the vacuum are investigated in various asymptotic regions of the parameters. The vacuum forces acting on the boundaries are presented as the sum of self-action and interaction terms. It is shown that the interaction forces between the separate parts of the boundary are always attractive. The generalization to the case of a scalar field with Neumann boundary condition is discussed.