On the approximation of the δ-shell interaction for the 3-D Dirac operator

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