Impact of space-time curvature coupling on the vacuum energy induced by a magnetic topological defect in flat space-time of arbitrary dimension

Abstract

We have investigated vacuum polarization of a quantized charged massive scalar field in the presence of a magnetic topological defect, modeled as an impenetrable tube of finite thickness carrying magnetic flux. At the tube's surface, we imposed a general Robin boundary condition. Our analysis demonstrates that, in flat space-time, the total induced vacuum energy is independent of the coupling $\xi$ of the scalar field's interaction with the space-time curvature only in the special cases of Dirichlet and Neumann boundary conditions. For general Robin boundary conditions, however, the total induced vacuum energy depends on the coupling $\xi$ in a flat space-time and exhibits a nontrivial dependence on the parameter of the Robin boundary condition. We investigated the dependence of this effect not only on Robin's boundary condition parameter, but also on the tube thickness and the space-time dimensionality. We conclude that careful measurements of vacuum polarization effects in flat space-time may, in principle, provide an independent way to probe the $\xi$ coupling.

arXiv comment19 pages, 3 figures

References in corpus (20)

• New Developments in the Casimir Effect
• Cosmic strings
• Size, Shape and Low Energy Electronic Structure of Carbon Nanotubes
• Heat kernel expansion: user's manual
• Inflation and quintessence with nonminimal coupling
• CMB constraints on cosmic strings and superstrings
• The Casimir effect for thin plasma sheets and the role of the surface plasmons
• Electronic properties of graphene with a topological defect
• The Casimir-Aharonov-Bohm effect?
• Direct Higgs-gravity interaction and stability of our Universe
• Polarization of the vacuum of a quantized scalar field by an impenetrable magnetic vortex of finite thickness
• Induced vacuum energy-momentum tensor in the background of a d-2 - brane in d+1 - dimensional space-time
• Vacuum energy induced by an impenetrable flux tube of finite radius
• Induced vacuum magnetic flux in quantum spinor matter in the background of a topological defect in two-dimensional space
• Casimir energy and force induced by an impenetrable flux tube of finite radius
• Properties of the ground state of electronic excitations in carbon-like nanocones
• Magnetic flux in the vacuum of quantum bosonic matter in the cosmic string background
• Testing Gravity and Predictions Beyond the Standard Model at Short Distances: The Casimir Effect
• Induced vacuum energy density of quantum charged scalar matter in the background of an impenetrable magnetic tube with the Neumann boundary condition
• Dependence of scalar matter vacuum energy, induced by a magnetic topological defect, on the coupling to space-time curvature