Abstract: 
In this talk two approximation problems for three dimensional Dirac operators with singular $\delta$-shell potentials supported on compact surfaces are discussed. The first one is a generalization of a result by Gesztesy and \v{S}eba, saying that a family of one dimensional Dirac operators with a special combination of electrostatic and Lorentz scalar $\delta$-interactions converges in the nonrelativistic limit to a Schr\"odinger operator with a $\delta'$-interaction. In the higher dimensional setting a similar convergence is obtained, but the limit operator is a Schr\"odinger operator with oblique jump conditions which is - for attractive interaction strengths - not semibounded from below.
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The second part of the talk is devoted to the approximation of Dirac operators with $\delta$-shell interactions by Dirac operators with scaled regular potentials in the norm resolvent sense. It will be explained how this can be achieved for special interaction strengths.
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This talk is based on joint works with J. Behrndt, C. Stelzer, and G. Stenzel.