标题： 几何相位刻画算子代数和缺失信息 显示英文标题

标题： Geometric Phases Characterise Operator Algebras and Missing Information

摘要： 我们展示了如何利用几何相位来完全描述量子系统（无论是否有引力），并通过提供关于其希尔伯特空间的几何和拓扑的信息来实现这一点。 我们发现了几何相位与冯·诺依曼代数之间的直接关系。 特别是，我们证明了零几何相位意味着该代数上存在一个定义良好的迹函数。 我们讨论了在AdS/CFT对应中如何针对永恒黑洞实现这一点。 另一方面，非零几何相位表明局部观察者缺失信息，这与仅覆盖所考虑量子系统的部分参考系有关。 我们通过几个例子来说明这一点，从磁场中的单个自旋到Virasoro Berry相位以及AdS时空中的永恒黑洞相关的几何相位。 对于后者，非零几何相位与相关冯·诺依曼代数的存在中心密切相关。 显示英文摘要

摘要： We show how geometric phases may be used to fully describe quantum systems, with or without gravity, by providing knowledge about the geometry and topology of its Hilbert space. We find a direct relation between geometric phases and von Neumann algebras. In particular, we show that a vanishing geometric phase implies the existence of a well-defined trace functional on the algebra. We discuss how this is realised within the AdS/CFT correspondence for the eternal black hole. On the other hand, a non-vanishing geometric phase indicates missing information for a local observer, associated to reference frames covering only parts of the quantum system considered. We illustrate this with several examples, ranging from a single spin in a magnetic field to Virasoro Berry phases and the geometric phase associated to the eternal black hole in AdS spacetime. For the latter, a non-vanishing geometric phase is tied to the presence of a centre in the associated von Neumann algebra.