AI 中文总结
研究德西特静态补丁全息术，通过沿观察者世界线插入算符计算两点函数和OTOCs检验相关推测，扩展OTOC计算并纳入相关因素，发现OTOC与迹的循环性和正定性冲突。
AI 中文摘要
我们研究了德西特静态补丁全息术的一个版本，其中带有观察者世界线的欧几里得引力路径积分被推测用于计算一个迹。受来自球面路径积分的该推测近期证据的启发，我们通过沿观察者世界线插入算符并计算两点函数和非时序四点关联函数（OTOCs）来进一步检验它。我们使用冲击波形式主义扩展了科尔奇迈尔和刘早期的OTOC计算，纳入了观察者反冲和引力反作用。我们发现OTOC与希尔伯特空间中迹的两个基本性质：循环性和正定性相冲突。冲击波几何的信号特征导致了微扰程函展开的两种不同重求和，它们通过循环性相互交换。正定性被违反是因为主导的微扰贡献导致（正则化的）OTOC增加。
英文摘要
We study a version of de Sitter static patch holography in which the Euclidean gravitational path integral, with an observer worldline included, is conjectured to compute a trace. Motivated by recent evidence for this conjecture from the sphere path integral, we test it further by inserting operators along the observer worldline and computing two-point functions and out-of-time-ordered four-point correlators (OTOCs). We extend an earlier OTOC calculation by Kolchmeyer and Liu using the shockwave formalism, incorporating both observer recoil and gravitational backreaction. We find that the OTOC conflicts with two basic properties of a trace in a Hilbert space: cyclicity and positivity. The signaling feature of the shockwave geometry gives rise to two distinct resummations of the perturbative eikonal expansion, which are interchanged by cyclicity. Positivity is violated by the fact that the leading perturbative contribution causes the (regularized) OTOC to increase.
Comments30 pages plus appendices
