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 D₀+|Fδ _Σ Gδ _Σ | D 0 + | F δ Σ ⟩ ⟨ G δ Σ | , where D₀ D 0 is the free Dirac operator, F and G are matrix valued coefficients, and δ _Σ δ Σ stands for the single layer distribution supported on a hypersurface Σ Σ , 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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Heriban et al. (2024) studied this question.
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