Non-self-adjoint relativistic point interaction in one dimension

The one-dimensional Dirac operator with a singular interaction term which is formally given by A?|?0???0|, where A an arbitrary 2×2 matrix and ?0 stands for the distribution, introduced as closed not necessarily self-adjoint operator. We study its spectral properties, find non-relativistic limit also address question of regular approximations. In particular, we show that, contrary to case local approximations, non-local approximating potentials, coupling constants are renormalized in limit.