Approximation of Dirac operators with $\hat{\mathbf{I}}´$-shell potentials in the norm resolvent sense, I. Qualitative results

Abstract

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

To appear in Math. Nachr