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

TL;DR

This paper investigates the quantum behavior of a massless spinor field around a singular magnetic vortex in 2+1 dimensions, using self-adjoint extensions to determine vacuum polarization effects and symmetry properties.

Contribution

It introduces a comprehensive analysis of boundary conditions via self-adjoint extensions for the Dirac Hamiltonian in a vortex background, elucidating vacuum polarization and symmetry breaking.

Findings

Vacuum polarization effects are fully characterized under general boundary conditions.

No anomaly is found in the quantization process.

Patterns of parity and chiral symmetry breaking are identified.

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, 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.