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Approximation of Dirac operators with $\boldsymbol{\delta}$-shell potentials in the norm resolvent sense, I. Qualitative results
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abstract
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.
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Approximation of Dirac operators with confining electrostatic and Lorentz scalar $\delta$-shell potentials
Confining Dirac delta-shell operators, previously inaccessible, are shown to be norm resolvent limits of strongly localized potentials with diverging interaction strengths.
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