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arXiv · 2311.02638

Non-local relativistic $\delta$-shell interactions

Lukáš Heriban·Matěj Tušek
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Abstract

In this paper, new self-adjoint realizations of the Dirac operator in dimension two and three are introduced. It is shown that they may be associated with the formal expression $\mathcal{D}_0+|F\delta_\Sigma\rangle\langle G\delta_\Sigma|$, where $\mathcal{D}_0$ is the free Dirac operator, $F$ and $G$ are matrix valued coefficients, and $\delta_\Sigma$ stands for the single layer distribution supported on a hypersurface $\Sigma$, and that they can be understood as limits of the Dirac operators with scaled non-local potentials. Furthermore, their spectral properties are analysed.

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Lukáš Heriban, Matěj Tušek. 2023-11-05. Non-local relativistic $\delta$-shell interactions. https://arxiv.org/abs/2311.02638

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