论文标题
部分可观测时空混沌系统的无模型预测
An approximate local modular quantum energy inequality in general quantum field theory
论文作者
论文摘要
对于每个局部量子场理论，假设REEH-SCHLIEDER特性，状态的局部制备性以及能量密度作为运算符值分布的静态，全球双曲线时空的任意维度，我们证明了近似量子的量子不等式的近似量子不等式。量子场理论由可观察到的von Neumann代数的网络给出，并假定能量密度可以满足多项式能量界限并在局部生成时间翻译。虽然近似于它是由依赖相应状态向量的小参数控制的，但派生的下限对时空平均能量密度的期望值具有通用结构。特别是，结合与与本地von Neumann代数相关的Tomita-Takesaki模块化算子直接相关。这揭示了静态空间上大类量子场理论的量子能不平等的一般，独立的特征。
For every local quantum field theory on a static, globally hyperbolic spacetime of arbitrary dimension, assuming the Reeh-Schlieder property, local preparability of states, and the existence of an energy density as operator-valued distribution, we prove an approximate quantum energy inequality for a dense set of vector states. The quantum field theory is given by a net of von Neumann algebras of observables, and the energy density is assumed to fulfill polynomial energy bounds and to locally generate the time translations. While being approximate in the sense that it is controlled by a small parameter that depends on the respective state vector, the derived lower bound on the expectation value of the spacetime averaged energy density has a universal structure. In particular, the bound is directly related to the Tomita-Takesaki modular operators associated to the local von Neumann algebras. This reveals general, model-independent features of quantum energy inequalities for a large class of quantum field theories on static spacetimes.
