Local Casimir Energy for a Wedge with circular outer boundary

TL;DR

This paper calculates the local Casimir energy in a wedge with a circular boundary for a massless scalar field, addressing boundary effects, divergences, and potential applications to cosmic strings.

Contribution

It introduces a regularization method using a generalized Abel-Plana formula to analyze local Casimir energy with boundary conditions in wedge geometries.

Findings

Derived expressions for vacuum energy density near boundaries.

Analyzed surface divergences in energy density.

Results applicable to cosmic string models.

Abstract

The local Casimir energy is investigated for a wedge with and without a circular outer boundary due to the confinement of a massless scalar field with general curvature coupling parameter and satisfying the Dirichlet boundary conditions. Regularization procedure is carried out making use of a variant of the generalized Abel-Plana formula, previously established by one of the authors. The surface divergences in the vacuum expectation values of the energy density near the boundaries are considered. The corresponding results can be applied to the cosmic strings.