On the approximation of the $\delta$-shell interaction for the 3-D Dirac operator

Abstract

We consider the three-dimensional Dirac operator coupled with a combination of electrostatic and Lorentz scalar $\delta$-shell interactions. We approximate this operator with general local interactions $V$. Without any hypotheses of smallness on the potential $V$, converges in the strong resolvent sense to the Dirac Hamiltonian coupled with a $\delta$-shell potential supported on $\S$, a bounded smooth surface. However, the coupling constant depends nonlinearly on the potential $V.$