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 \(L^2(\Omega ;{\mathbb {C}}^4)\) for any open set \(\Omega \subset {\mathbb {R}}^3\) 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 \(\pm \infty \) and one additional eigenvalue of infinite multiplicity.

在本说明中，研究了带有边界条件的三维Dirac算子\（A_m \），它们是二维之字形边界条件的类似物。结果表明，\（A_M \）是自伴随在\（L ^ 2（\欧米茄; {\ mathbb {C}} ^ 4）\）对于任何打开的组\（\欧米茄\子集{\ mathbb {R }} ^ 3 \）及其谱是根据\（\ Omega \）中Dirichlet Laplacian的谱来明确描述的。尤其是，只要Dirichlet拉普拉斯算子的谱是纯离散的，则\（A_m \）的谱也由以\（\ pm \ infty \）累积的离散特征值和一个无限多重性的附加特征值组成。