On the contribution of the coulomb singularity of arbitrary charge to the dirac hamiltonian

We study the self-adjoint extensions of the Dirac operator a (p -B)+ μ₀ -W, where the electrical potential W contains a Coulomb singularity of arbitrary charge and the magnetic potential B is allowed to be unbounded at infinity. We show that if the Coulomb singularity has the form v(r)/r where v has a limit at 0, then, for any self-adjoint extension of the Dirac operator, removing the singularity results in a Hubert-Schmidt perturbation of its resolvent.