Approximation of Dirac operators with δ${\delta }$‐shell potentials in the norm resolvent sense. I. Qualitative results

Jussi Behrndt, Markus Holzmann and Christian Stelzer‐Landauer

Mathematische Nachrichten, 2025, vol. 298, issue 8, 2499-2546

Abstract: In this paper, the approximation of Dirac operators with general δ$\delta$‐shell potentials supported on C2$C^2$‐curves in R2$\mathbb {R}^2$ or C2$C^2$‐surfaces in R3$\mathbb {R}^3$, which may be bounded or unbounded, is studied. It is shown under suitable conditions on the weight of the δ$\delta$‐interaction that a family of Dirac operators with regular, squeezed potentials converges in the norm resolvent sense to the Dirac operator with the δ$\delta$‐shell interaction.

Date: 2025
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