Pauli Hamiltonians with an Aharonov–Bohm flux

Abstract

We study a two-dimensional Pauli operator describing a charged quantum particle with spin $1/2$ moving on a plane in presence of an orthogonal Aharonov–Bohm magnetic flux. We classify all the admissible self-adjoint realizations and give a complete picture of their spectral and scattering properties. Symmetries of the resulting Hamiltonians are also discussed, as well as their connection with the Dirac operator perturbed by an Aharonov–Bohm singularity.