Relativistic point interactions: Approximation by smooth potentials

We show that the four-parameter family of one-dimensional relativistic point interactions studied by Benvegnù and Da̧browski may be approximated in the strong resolvent sense by smooth, local, short-range perturbations of the Dirac Hamiltonian. In addition, we prove that the nonrelativistic limits correspond to the Schrödinger point interactions studied extensively by the author and Paul Chernoff.