AI 中文总结
研究半有界算子本质自伴性，通过描述基于趋近恒等算子有界性定义的局部准则，构建抽象算子理论框架，推广相关方法，并应用于多粒子薛定谔算子等，获得本质自伴性的有竞争力结果。
AI 中文摘要
一个下方被一界定的半有界算子，若其伴随算子的核是平凡的，则本质自伴。若伴随算子的核属于弗里德里希斯扩张的形式域，就是这种情况。我们描述了此准则的一个局部版本，其中局部性依据趋近恒等算子的有界算子来定义。结果是一个抽象算子理论框架，推广了维恩霍尔茨和西马德在半有界椭圆型偏微分算子背景下发展的方法。作为应用，我们在多粒子薛定谔算子、伪相对论哈密顿量以及非相对论量子电动力学标准模型的本质自伴性方面得到了有竞争力的结果。
英文摘要
A semi-bounded operator that is bounded below by one is essentially self-adjoint if the kernel of the adjoint is trivial. This is the case if the kernel of the adjoint belongs to the form domain of the Friedrichs extension. We describe a local version of this criterion, where locality is defined in terms of bounded operators approaching the identity. The result is an abstract operator theoretic framework that generalizes the method by Wienholtz and Simader developed in the context of semi-bounded elliptic partial differential operators. As applications, we obtain competitive results on essential self-adjointness of many-particle Schrödinger operators, pseudo-relativistic Hamiltonians, and the standard model of non-relativistic quantum electrodynamics.
Comments18 pages
