  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.
