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arXiv · 1902.03901

Dirac operators and shell interactions: a survey

Thomas Ourmières-Bonafos·Fabio Pizzichillo
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Abstract

In this survey we gather recent results on Dirac operators coupled with $\delta$-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterward we switch to an approximation question: can these operators be recovered as limits of Dirac operators coupled with squeezing potentials ? We also discuss spectral features of these models. Namely, we recall the main spectral consequences of a resolvent formula and conclude the survey by commenting a result of asymptotic nature for the eigenvalues in the gap of a Dirac operator coupled with a Lorentz-scalar interaction.

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Thomas Ourmières-Bonafos, Fabio Pizzichillo. 2019-02-11. Dirac operators and shell interactions: a survey. https://arxiv.org/abs/1902.03901

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