量子场论中的量子能量不等式和稳定性条件
Quantum Energy Inequalities and Stability Conditions in Quantum Field Theory
摘要：
我们简要回顾了量子能量不等式（QEI），然后讨论了两条工作线，这两条工作线表明QEI与量子场论的各种自然性质密切相关，这些性质都可以被视为稳定性条件。第一个是基于与Verch的联合工作，并绘制微观稳定性（微观局部谱条件），介观稳定性（QEI）和宏观稳定性（被动性）之间的联系。第二个方向考虑了可数个大质量标量场的量子反作用，并将量子反作用的存在性和标度性质与质量谱联系起来。结果是，存在一个合适的QEI与多项式标度是一个充分条件的模型，以满足Buchholz-Wichmann核性准则。我们简要地讨论了正在进行的工作与大岛和波尔曼，旨在获得更深入的了解这种关系。
英文摘要：
We give a brief review of quantum energy inequalities (QEIs) and then discuss two lines of work which suggest that QEIs are closely related to various natural properties of quantum field theory which may all be regarded as stability conditions. The first is based on joint work with Verch, and draws connections between microscopic stability (microlocal spectrum condition), mesoscopic stability (QEIs) and macroscopic stability (passivity). The second direction considers QEIs for a countable number of massive scalar fields, and links the existence and scaling properties of QEIs to the spectrum of masses. The upshot is that the existence of a suitable QEI with polynomial scaling is a sufficient condition for the model to satisfy the Buchholz--Wichmann nuclearity criterion. We briefly discuss on-going work with Ojima and Porrmann which seeks to gain a deeper understanding of this relationship.
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