Self-adjointness of the two-dimensional massless Dirac Hamiltonian and vacuum energy density in the background of a singular magnetic vortex

TL;DR

This paper investigates the self-adjointness and vacuum energy density of a massless Dirac Hamiltonian in 2+1 dimensions with a singular magnetic vortex, using self-adjoint extensions to define boundary conditions.

Contribution

It introduces a comprehensive analysis of boundary conditions for the Dirac Hamiltonian in a vortex background and computes the resulting vacuum energy density.

Findings

Vacuum energy density depends on boundary conditions at the vortex

Self-adjoint extensions provide a physically consistent framework

Explicit formulas for energy density in the vortex background

Abstract

A massless spinor field is quantized in the background of a singular static magnetic vortex in 2+1-dimensional space-time. The method of self-adjoint extensions is employed to define the most general set of physically acceptable boundary conditions at the location of the vortex. Under these conditions, the vacuum energy density and effective potential in the vortex background are determined.