We study density matrices in quantum gravity, focusing on topology change. We argue that the inclusion of bra-ket wormholes in the gravity path integral is not a free choice, but is dictated by the specification of a global state in the multi-universe Hilbert space. Specifically, the Hartle-Hawking (HH) state does not contain bra-ket wormholes. It has recently been pointed out that bra-ket wormholes are needed to avoid potential bags-of-gold and strong subadditivity paradoxes, suggesting a problem with the HH state. Nevertheless, in regimes with a single large connected universe, approximate bra-ket wormholes can emerge by tracing over the unobserved universes. More drastic possibilities are that the HH state is non-perturbatively gauge equivalent to a state with bra-ket wormholes, or that the third-quantized Hilbert space is one-dimensional. Along the way we draw some helpful lessons from the well-known relation between worldline gravity and Klein-Gordon theory. In particular, the commutativity of boundary-creating operators, which is necessary for constructing the alpha states and having a dual ensemble interpretation, is subtle. For instance, in the worldline gravity example, the Klein-Gordon field operators do not commute at timelike separation.

中文翻译：

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量子引力中的密度矩阵

我们研究量子引力中的密度矩阵，关注拓扑变化。我们认为，在重力路径积分中包含Brackket虫洞不是一个自由选择，而是由多宇宙Hilbert空间中的全局状态的规范所决定的。具体而言，哈特·霍金（HH）状态不包含盲目虫洞。最近已经指出，需要使用蠕虫孔来避免潜在的金袋和强烈的亚可加性悖论，这提示HH状态存在问题。然而，在具有单个大连通宇宙的系统中，通过追踪未观察到的宇宙，可能会出现近似的bra虫洞。更大的可能性是HH状态是非扰动规范的，等效于带有Brackket虫洞的状态，或者第三量化的希尔伯特空间是一维的。在此过程中，我们从世界重力与Klein-Gordon理论之间的众所周知的关系中吸取了一些有益的教训。特别地，边界生成算子的可交换性是微妙的，这对于构造α态并具有双重整体解释是必需的。例如，在世界重力示例中，Klein-Gordon场算子不在时空分离时上下班。