标题： 非局部相对论$δ$-壳相互作用 显示英文标题

标题： Non-local relativistic $δ$-shell interactions

摘要： 本文引入了二维和三维中狄拉克算子的新自伴实现。 证明了它们可以与形式表达式 $\mathcal{D}_0+|F\delta_\Sigma\rangle\langle G\delta_\Sigma|$ 相关联，其中 $\mathcal{D}_0$ 是自由狄拉克算子， $F$ 和 $G$ 是矩阵值系数，而 $\delta_\Sigma$ 表示支撑在一个超曲面 $\Sigma$ 上的单层分布，并且它们可以被理解为具有缩放非局部势的狄拉克算子的极限。 此外，分析了它们的谱性质。 显示英文摘要

摘要： In this paper, new self-adjoint realizations of the Dirac operator in dimension two and three are introduced. It is shown that they may be associated with the formal expression $\mathcal{D}_0+|F\delta_\Sigma\rangle\langle G\delta_\Sigma|$, where $\mathcal{D}_0$ is the free Dirac operator, $F$ and $G$ are matrix valued coefficients, and $\delta_\Sigma$ stands for the single layer distribution supported on a hypersurface $\Sigma$, and that they can be understood as limits of the Dirac operators with scaled non-local potentials. Furthermore, their spectral properties are analysed.