Approximation of Dirac operators with δ‐shell potentials in the norm resolvent sense, II: Quantitative results

Abstract This paper is devoted to the approximation of two‐ and three‐dimensional Dirac operators with combinations of electrostatic and Lorentz scalar ‐shell interactions in the norm resolvent sense. Relying on results from Behrndt, Holzmann, and Stelzer‐Landauer Math. Nachr. 298 (2025), 2499–2546, an explicit smallness condition on the coupling parameters is derived so that is the limit of Dirac operators with scaled electrostatic and Lorentz scalar potentials. Via counterexamples it is shown that this condition is sharp. The approximation of for larger coupling constants is achieved by adding an additional scaled magnetic term.