Whightman function and scalar Casimir densities for a wedge with a cylindrical boundary

TL;DR

This paper analyzes the quantum vacuum effects for a scalar field in a wedge with a cylindrical boundary, deriving the Wightman function and energy-momentum tensor, and examining boundary-induced forces and asymptotic behaviors.

Contribution

It provides a detailed calculation of vacuum expectation values and forces in a wedge with a cylindrical boundary, including new insights into boundary-induced effects and asymptotic behaviors.

Findings

Vacuum forces on wedge sides are attractive due to the cylindrical boundary.

Expectation values are expressed as a sum of boundary-free and boundary-induced parts.

Asymptotic behaviors near boundaries are characterized.

Abstract

Whightman function, vacuum expectation values of the field square, and the energy-momentum tensor are investigated for a scalar field inside a wedge with and without a coaxial cylindrical boundary. Dirichlet boundary conditions are assumed on the bounding surfaces. The vacuum energy-momentum tensor is evaluated in the general case of the curvature coupling parameter. Making use of a variant of the generalized Abel-Plana formula, expectation values are presented as 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 this boundary. The asymptotic behaviour of the field square, vacuum energy density and stresses near the boundaries are investigated. 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. As a limiting case, the geometry of two parallel plates perpendicularly intersected by a third one is analyzed.