Non-Relativistic Limit for Matrix 1D-Dirac Operators with Point Interactions

Abstract We consider different $$c$$ -dependent realizations $${\mathbf{D}}_{X,{\mathbf{B}}_{c}}^{c}$$ of $$2m\times 2m$$ -Dirac operator with point interactions on a discrete set $$X$$ where $$c$$ is the velocity of light. Our main aim is to show that non-relativistic limit of $${\mathbf{D}}_{X,{\mathbf{B}}_{c}}^{c}$$ as $$c\to\infty$$ is an appropriate Schrödinger operator $${\mathbf{H}}_{X,{\mathbf{B}}_{H}}$$ with point interactions. This result extends the corresponding result from [16] to the matrix case. As a special case we establish that the non-relativistic limit of $$\delta^{\prime}$$ -realizations for $$2m\times 2m$$ -Dirac operator coincides with Schrödinger operator $${\mathbf{H}}_{X,{\mathbf{B}}_{H}}$$ with $$\delta^{\prime}$$ -interactions on the same set.