纠缠、观察者与宇宙学：冯·诺依曼代数的观点
Entanglement, Observers and Cosmology: a view from von Neumann Algebras
摘要：
当因果完备时空域上的量子场论是$III$型因子时，会出现无限纠缠涨落。在弱引力极限$G_N=0$下，通过加入一个物理参考系系统（观测者），该因子可转化为具有有限纠缠涨落的交叉乘积型$II$因子.使用物理参考系来定义发散纠缠的正则化在形式上与超选择电荷的量子信息方法相同。在这种情况下，添加的参考系允许不同超选择扇区之间的量子叠加。对于宇宙视界的情况下，我们映射到一个类型的$II$修改的纯de Sitter型$III$因子，我们使用这样定义的类型$II$有限纠缠波动来预测标量曲率波动的原始功率谱。对于Hagedorn高温相的大$N$杨米尔斯，类型$II$描述的Hagedorn相帐户，在大$N$限制，为相应的矩阵模型本征值分布的间隔的量子涨落。
英文摘要：
Infinite entanglement fluctuations appear when a quantum field theory on a causally complete domain of space-time is a type $III$ factor. In the weak gravity limit $G_N=0$ this factor can be transformed into a crossed product type $II$ factor with finite entanglement fluctuations by adding a physical reference frame system (observer). The use of a physical reference frame to define a regularization of divergent entanglement is formally identical to the quantum information approach to superselection charges. In that case the added reference frame allows quantum superpositions between different superselection sectors. For the case of cosmological horizons we map the primordial inflationary slow rolling phase into a type $II$ modification of the pure de Sitter type $III$ factor and we use the so defined type $II$ finite entanglement fluctuations to predict the primordial power spectrum of scalar curvature fluctuations. For the Hagedorn high temperature phase of large $N$ Yang Mills, the type $II$ description of the Hagedorn phase accounts, in the large $N$ limit, for the quantum fluctuations of the interval of the corresponding matrix model eigenvalue distribution.
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