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

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.