Induced vacuum magnetic flux in quantum spinor matter in the background of a topological defect in two-dimensional space

Abstract

A topological defect in the form of the Abrikosov-Nielsen-Olesen vortex is considered as a gauge-flux-carrying tube that is impenetrable for quantum matter. The relativistic spinor matter field is quantized in the vortex background in $2+1$-dimensional conical space-time which is a section orthogonal to the vortex axis; the most general set of boundary conditions ensuring the impenetrability of the vortex core is employed. We find the induced vacuum current circulating around the vortex and the induced vacuum magnetic field strength pointing along the vortex axis. The requirement of finiteness and physical plausibility for the total induced vacuum magnetic flux allows us to restrict the variety of admissible boundary conditions. The dependence of the results on the transverse size of the vortex, as well as on the vortex flux and the parameter of conicity, is elucidated.

53 pages, 10 figures, minor changes, discussion extended, some references added

References in corpus (4)

• Two Dimensional Atomic Crystals
• Fermionic current densities induced by magnetic flux in a conical space with a circular boundary
• Fermionic condensate in a conical space with a circular boundary and magnetic flux
• Constraints on Brane Inflation and Cosmic Strings

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• Induced vacuum current and magnetic flux in quantum scalar matter in the background of a vortex defect with the Neumann boundary condition
• Casimir effect for fermion condensate in conical rings
• Dependence of scalar matter vacuum energy, induced by a magnetic topological defect, on the coupling to space-time curvature
• Induced vacuum magnetic field in the cosmic string background
• Impact of space-time curvature coupling on the vacuum energy induced by a magnetic topological defect in flat space-time of arbitrary dimension
• Magnetic field in vacuum of quantum spinor matter induced by a cosmic string in three-dimensional space