Self-adjointness of the two-dimensional massless Dirac Hamiltonian and vacuum polarization effects 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, all effects of polarization of the massless fermionic vacuum in the vortex background are determined. Absence of anomaly is demonstrated, and patterns of both parity and chiral symmetry breaking are discussed.