Non-local relativistic $\delta$-shell interactions

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 ${\mathcal{D}}_0+\mathrm{\mid }F{\delta }_{\mathrm{\Sigma }}⟩⟨G{\delta }_{\mathrm{\Sigma }}\mathrm{\mid }$, where ${\mathcal{D}}_0$ is the free Dirac operator, $F$ and $G$ are matrix valued coefficients, and ${\delta }_{\mathrm{\Sigma }}$ stands for the single layer distribution supported on a hypersurface $\mathrm{\Sigma }$, and that they can be understood as limits of the Dirac operators with scaled non-local potentials. Furthermore, their spectral properties are analysed.