To the Spectral Theory of One-Dimensional Matrix Dirac Operators with Point Matrix Interactions¹

Abstract—We investigate one-dimensional ($2p \times 2p$)-matrix Dirac operators ${{D}_{{X,\alpha }}}$ and ${{D}_{{X,\beta }}}$ with point matrix interactions on a discrete set $X$. Several results of [4] are generalized to the case of ($p \times p$)-matrix interactions with $p > 1$. It is shown that a number of properties of the operators ${{D}_{{X,\alpha }}}$ and ${{D}_{{X,\beta }}}$ (self-adjointness, discreteness of the spectrum, etc.) are identical to the corresponding properties of some Jacobi matrices ${{B}_{{X,\alpha }}}$ and ${{B}_{{X,\beta }}}$ with ($p \times p$)-matrix entries. The relationship found is used to describe these properties as well as conditions of continuity and absolute continuity of the spectra of the operators ${{D}_{{X,\alpha }}}$ and ${{D}_{{X,\beta }}}$ . Also the non-relativistic limit at the velocity of light $c \to \infty $ is studied.