Smooth Approximation of Finitely-Many Relativistic Point Interactions Walter B. Huddell III Department of Mathematics Eastern University St. Davids, PA 19087 Rhonda J. Hughes Department of Mathematics Bryn Mawr College Bryn Mawr, PA 19010 Abstract. The purpose of this paper is to show that finitely-many relativistic point interac- tions 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. 1