Approximation of Dirac operators with \boldsymbolδ-shell potentials in the norm resolvent sense, I. Qualitative results

2023/08/25 by Behrndt, Jussi, Holzmann, Markus, Stelzer, Christian
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2308.13344

Abstract

In this paper the approximation of Dirac operators with general δ-shell potentials supported on C²-curves in ℝ² or C²-surfaces in ℝ³, which may be bounded or unbounded, is studied. It is shown under suitable conditions on the weight of the δ-interaction that a family of Dirac operators with regular, squeezed potentials converges in the norm resolvent sense to the Dirac operator with the δ-shell interaction.

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