Dependence of scalar matter vacuum energy, induced by a magnetic topological defect, on the coupling to space-time curvature

TL;DR

This paper investigates how the vacuum energy of a charged scalar field around a magnetic topological defect varies with the field's coupling to space-time curvature, revealing dependence on boundary conditions and coupling in flat space.

Contribution

It demonstrates that the total vacuum energy's dependence on curvature coupling varies with boundary conditions, especially for Robin boundary conditions, in flat space-time.

Findings

Total vacuum energy is independent of curvature coupling for Dirichlet and Neumann conditions.

For Robin boundary conditions, the energy depends on the coupling for certain parameter ranges.

Dependence on coupling is observed only for negative Robin boundary parameters.

Abstract

We considered the vacuum polarization of a quantized charged scalar matter field in the background of a topological defect modeled by a finite-thickness tube with magnetic flux inside. The tube is impenetrable for quantum matter, and a generalized boundary condition of the Robin type is imposed at its surface. We have shown that in the flat space-time, the total induced vacuum energy does not depend on the coupling $(\xi)$ of the scalar field's interaction with the space-time curvature, only for the partial cases of the Dirichlet and Neumann boundary conditions on the tube's edge. However, for generalized Robin boundary conditions, the total induced energy depends on the coupling $\xi$ in flat space-time, at least for negative values of the boundary condition parameter $-\pi/2<\theta<0$.