Approximation of Dirac operators with \(\boldsymbol{\delta}\)-shell potentials in the norm resolvent sense

In this paper the approximation of Dirac operators with general \(\delta\)-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 \(\delta\)-interaction that a family of Dirac operators with regular, squeezed potentials converges in the norm resolvent sense to the Dirac operator with the \(\delta\)-shell interaction.