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

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.