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

Abstract

We investigate one-dimensional (2p × 2p)-matrix Dirac operators DX,α and DX,β with point matrix interactions on a discrete set X. Several results of [4] are generalized to the case of (p × p)-matrix interactions with p > 1. It is shown that a number of properties of the operators DX,α and DX,β (self-adjointness, discreteness of the spectrum, etc.) are identical to the corresponding properties of some Jacobi matrices BX,α and BX,β with (p × 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 DX,α and DX,β. Also the non-relativistic limit at the velocity of light c → ∞ is studied.