Non-local relativistic δ-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 D-0+|F delta(Sigma)>< G delta(Sigma)|, where 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.