AI 中文总结
研究动态量子引力中观察者体验，将一维量子力学系统与欧几里得 AdS JT 引力耦合，推导圆盘拓扑下相关表达式及波动情况，讨论全息解释与洛伦兹解释，还计算双喇叭对观察者配分函数的贡献。
AI 中文摘要
受理解动态量子引力中观察者体验问题的推动，我们研究了生活在体世界线上的一维量子力学系统与欧几里得 AdS JT 引力耦合的效应。在圆盘拓扑中（世界线在两个边界点之间延伸），我们推导了观察者欧几里得传播子及其关联函数的确切表达式，并讨论了它们的全息解释。对量子力学的主要影响是观察者演化的总欧几里得时间的波动，或封闭欧几里得路径的逆温度波动。这将标准量子力学演化算符转变为这些算符的平均值，由欧几里得时间上的测度加权，在半经典极限下该测度在边界点之间的测地距离附近达到峰值。我们刻画了围绕该值的波动，发现它们相对于平均值较小，但相对于模型的有效普朗克尺度较大。具有精细间隔态密度的观察者可以分辨这些波动。我们还讨论了这些欧几里得计算的洛伦兹解释。最后，我们计算了来自双喇叭对与引力耦合的观察者配分函数的贡献。在这种情况下，有效温度的波动很大，反映出不存在平滑的半经典鞍点。
英文摘要
Motivated by the problem of understanding the experience of an observer in dynamical quantum gravity, we study the effects of coupling a one-dimensional quantum mechanical system living on a bulk worldline to Euclidean AdS JT gravity. On the disk topology, where the worldline stretches between two boundary points, we derive exact expressions for the Euclidean propagator of the observer and for its correlation functions, and discuss their holographic interpretation. The main effect on the quantum mechanics is the fluctuation of the total Euclidean time for which the observer evolves, or its inverse temperature for closed Euclidean paths. This turns the standard quantum mechanical evolution operator into an average of those, weighted by a measure over Euclidean times which in the semiclassical limit is peaked around the geodesic distance between the boundary points. We characterize the fluctuations around this value, finding that they are small compared to the mean, but large compared to the effective Planck scale of the model. These fluctuations can be resolved by an observer with a finely spaced density of states. We also discuss the Lorentzian interpretation of these Euclidean calculations. Finally, we compute a contribution to the partition function of the observer coupled to gravity coming from the double trumpet. In this case the fluctuations of the effective temperature are large, reflecting the absence of a smooth semiclassical saddle point.
Comments32 pages + appendices
