关系路径积分、有效作用量与量子框架协变性
Relational path integral, effective actions and quantum frame covariance in gravity
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中文总结 AI 辅助
该研究借助量子参考系，提出引力路径积分的关系丛几何表述，得到规范不变路径积分，消除规范固定需求，具QRF变化协变性，有新真空谱等预测，还构建了规范不变有效作用量，为重整化关系定义奠基。
中文摘要 AI 辅助
我们通过引入量子参考系（QRFs）这一新工具，提出了引力路径积分的一种关系丛几何表述。在引力中，QRFs是由可用场内容构建的规范协变坐标系。用关系可观测量表述，得到了一个明显规范不变的无鬼和无反常的路径积分，其中可观测量及其关联函数在一个框架内是局域的。它消除了规范固定的需要，等同于QRF被规范固定的Faddeev - Popov版本，恢复了某些先前的提议。关键特性是其在QRF变化下的协变性：它是一个视角中性路径积分，编码了所有内部QRF视角及其间的变换。这导致了几个定性预测：一个QRF视角下关系可观测量的局域关联函数和时间演化在另一个视角下会变得模糊，并且出现了新的关系真空谱。由依赖框架的无边界和渐近基态组成，一个视角下的真空在另一个视角下通常会呈现激发态。最后，我们通过仅将源与关系可观测量耦合来构建规范不变但依赖框架的有效作用量，为重整化的关系定义奠定基础。
英文摘要
We propose a relational bundle-geometric formulation of the gravitational path integral by invoking the new tool of quantum reference frames (QRFs), which in gravity are gauge-covariant coordinate systems constructed from the available field content. Formulated in terms of relational (frame-dressed) observables, this yields a manifestly gauge-invariant path integral without ghosts and anomalies, and in which observables and their correlators are local to a frame. While eliminating the need for gauge fixing, it is equivalent to Faddeev-Popov versions in which the QRF is gauge-fixed, recovering certain previous proposals. A key feature is its covariance under QRF changes: it is a perspective-neutral path integral which encodes all internal QRF perspectives and the transformations between them. This leads to several qualitative predictions: local correlators and time evolution of relational observables in one QRF perspective become fuzzy in another, and a new spectrum of relational vacua arises. Comprised of frame-dependent no-boundary and asymptotic ground states, a vacuum from one perspective appears generally excited in another. Finally, we construct gauge-invariant, yet frame-dependent effective actions by coupling sources exclusively to relational observables, setting the stage for a relational definition of renormalization.
