Smooth approximation of finitely many relativistic point interactions

Abstract

The purpose of this paper is to show that finitely many relativistic point interactions may be approximated in the strong resolvent sense by sequences of operators with smooth potentials. We consider the entire family of relativistic point interactions, and determine those for which renormalization of the coupling constant occurs when the corresponding potentials are approximated by finitely many local, short-range perturbations of the free Dirac operator.