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
- National Higher School of Mathematics（国立高等数学学校）
- Carl von Ossietzky Universität Oldenburg（奥尔登堡卡尔·冯·奥西茨基大学）
- POEMS, CNRS, Inria, ENSTA, Institut Polytechnique de Paris（巴黎理工学院 POEMS 联合实验室（CNRS、Inria、ENSTA））
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
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。
中文摘要 AI 辅助
本文致力于研究在任意维数下具有紧致Lipschitz边界的欧几里得区域中，满足MIT袋边界条件的Dirac算子。研究表明，此类算子在适当的定义域上是自伴的，并且可以在假设相关的Robin-Laplace特征值关于边界条件中的参数具有指定渐近行为的前提下，作为全空间中在区域外部带有大质量项的Dirac算子的范数-预解极限而恢复。该假设被证明对一类非光滑区域成立，这类区域包括凸区域，以及更一般地，可通过适当微分同胚进行“局部凸化”的区域。据我们所知，这代表了在预解收敛意义下，针对非光滑区域的MIT袋模型的首次无穷质量解释。借助最近建立的同余变换，大多数结果被推广到广义MIT袋边界条件。
英文摘要
The work is devoted to the study of Dirac operators with MIT bag boundary conditions in Euclidean domains with compact Lipschitz boundaries in arbitrary dimensions. It is shown that such operators are self-adjoint on suitable definition domains and can be recovered as the norm-resolvent limits of Dirac operators in the whole space with a large mass term outside the domain, under the assumption that an associated Robin-Laplacian eigenvalue has a prescribed asymptotic behavior with respect to a parameter in the boundary condition. This assumption is shown to hold for a class of non-smooth domains, which includes convex domains and, more generally, domains that can be "locally convexified" by suitable diffeomorphisms. To the best of our knowledge, this represents the first infinite mass interpretation for the MIT bag model in the sense of resolvent convergence for non-smooth domains. Most results are extended to the generalized MIT bag boundary conditions with the help of the recently established congruence transform.
