AI 中文总结
研究德西特空间中半经典观察者的可观测量代数，通过算符时间演化研究OTOC修正，探讨时钟处理方式对相关条件及代数的影响，推测代数对易子情况，还说明时间间隔超扰时间时OTOC变化及对全息术的挑战。
AI 中文摘要
我们研究了德西特空间中半经典观察者的可观测量代数。当算符通过一个扰乱时间进行时间演化时，由于宇宙学视界附近的冲击波散射，时间序外关联函数（OTOCs）会受到修正。当经典地处理观察者的时钟时，我们表明时间提前效应意味着物质算符真空关联函数的KMS条件失效。当观察者的时钟被量子化时，这意味着哈特尔 - 霍金态不是所得交叉积代数上的迹。我们推测观察者的代数有一个平凡的对易子。当算符之间的时间间隔超过扰乱时间时，OTOC衰减到零并出现一个自由积代数。我们用带有冲击波的德西特JT引力的经典解来说明这一点。我们评论了我们的结果如何对以观察者为中心的静态补丁全息术构成挑战。
英文摘要
We study the algebra of observables of a semiclassical observer in de Sitter space. When operators are time-evolved by a scrambling time, out-of-time-ordered correlation functions (OTOCs) receive corrections due to shockwave scattering near the cosmological horizon. When the observer's clock is treated classically, we show that the time advance effect implies the breakdown of the KMS condition for vacuum correlators of matter operators. When the observer's clock is quantized, this implies that the Hartle-Hawking state is not a trace on the resulting crossed-product algebra. We conjecture that the observer's algebra has a trivial commutant. When the time separation between operators exceeds the scrambling time, the OTOC decays to zero and a free product algebra emerges. We illustrate this using classical solutions of de Sitter JT gravity with shocks. We comment on how our results pose a challenge for observer-centric static patch holography.
