无界锥上MIT袋模型的自伴性

A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and delta-shell interactions

We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a $\mathcal{C}^2$-compact surface without boundary. To do so we are lead to study the layer potential induced by the Dirac system as well as to define traces in a weak sense for functions in the appropriate Sobolev space. Finally, we introduce Calderón projectors associated with the problem and illustrate the method in two special cases: the well-known MIT bag model and an electrostatic $δ$-shell interaction.

非光滑凸域中的MIT袋

MIT bag in non-smooth convex domains

本文证明非光滑凸域中MIT袋边界条件的Dirac算子自伴性，并作为大质量极限出现，推广了光滑域结果。

The MIT Bag Model as an infinite mass limit

The Dirac operator, acting in three dimensions, is considered. Assuming that a large mass $m>0$ lies outside a smooth and bounded open set $Ω\subset\R^3$, it is proved that its spectrum is approximated by the one of the Dirac operator on $Ω$ with the MIT bag boundary condition. The approximation, which is developed up to and error of order $o(1/\sqrt m)$, is carried out by introducing tubular coordinates in a neighborhood of $\partialΩ$ and analyzing the corresponding one dimensional optimization problems in the normal direction.

广义 MIT Bag 模型的非相对论极限与谱不等式

Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities

本文证明了受广义 MIT bag 边界条件约束的自伴 Dirac 算子在范数预解意义下的非相对论极限为 Dirichlet Laplacian，从而将后者的谱几何结果推广至大 $c$ 时的 Dirac 算子。

MIT袋模型与非光滑区域中的无穷质量极限

MIT bag model and infinite mass limit in non-smooth domains

本文研究非光滑区域上MIT袋边界条件的Dirac算子，证明其自伴性并作为全空间大质量项算子的范数-预解极限，首次在预解收敛意义下给出非光滑区域的无穷质量解释。

广义MIT袋模型向具有锯齿形边界条件的Dirac算子的收敛性

Convergence of generalized MIT bag models to Dirac operators with zigzag boundary conditions

本文研究广义MIT袋算子向锯齿型边界条件Dirac算子的预解式收敛，证明强收敛成立而范数收敛不成立，并指出唯一障碍是极限算子存在无限重特征值，投影到其正交补后可得范数收敛。