Matrix Representations of Dirac Operators With Finite Spectrum

ABSTRACT In this paper, we identify a class of Dirac equations such that for any Dirac operator problem composed of such an equation and an arbitrary separated or real coupled self‐adjoint boundary condition, it can be represented as an equivalent finite dimensional matrix eigenvalue problem. Conversely, given any matrix eigenvalue problem of a specific type and an appropriate separated or real coupled self‐adjoint boundary condition, we construct a class of Dirac operators with the specified boundary condition. Each of these Dirac operators is equivalent to the given matrix eigenvalue problem, where equivalence implies that they possess exactly the same eigenvalues.