A Note on the Three Dimensional Dirac Operator with Zigzag Type Boundary Conditions

摘要

In this note the three dimensional Dirac operator A(m) with boundary conditions, which are the analogue of the two dimensional zigzag boundary conditions, is investigated. It is shown that A(m) is self-adjoint in L-2(Omega; C-4) for any open set Omega subset of R-3 and its spectrum is described explicitly in terms of the spectrum of the Dirichlet Laplacian in Omega. In particular, whenever the spectrum of the Dirichlet Laplacian is purely discrete, then also the spectrum of A(m) consists of discrete eigenvalues that accumulate at +/-infinity and one additional eigenvalue of infinite multiplicity.