On the contribution of the Coulomb singularity of arbitrary charge to the Dirac Hamiltonian

Abstract

We study the self-adjoint extensions of the Dirac operator α ⋅ ( p − B ) + μ 0 β − W \alpha \cdot (p - B) + \mu _{0}\beta - W , where the electrical potential W W contains a Coulomb singularity of arbitrary charge and the magnetic potential B B is allowed to be unbounded at infinity. We show that if the Coulomb singularity has the form v ( r ) / r v(r)/r where v v has a limit at 0, then, for any self-adjoint extension of the Dirac operator, removing the singularity results in a Hilbert-Schmidt perturbation of its resolvent.