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arXiv 2105.02129hep-th
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量子力学中的虫洞

Wormholes in Quantum Mechanics

Herman Verlinde

摘要:

在通过量子化相空间得到的一般一维量子系统中,引入了虫洞配分函数的几何路径积分定义。在半经典极限和一些简单的例子中,我们计算了虫洞的配分函数。发现n重虫洞的配分函数与双系统热混合态的n阶Renyi熵相同。这种混合态结合了三种类型的量子统计行为:经典相关,量子纠缠和经典不相关。我们将我们的处方应用到具有Virasoro对称性的2D CFTs,并在AdS3引力方面恢复全息对偶公式。

英文摘要:

We introduce a geometric path integral definition of wormhole partition functions in a general class of 1D quantum systems obtained by quantizing a phase space. We compute the wormhole partition function in a semi-classical limit and in some simple examples. The partition function of the n-fold wormhole is found to be identical to the n-th Renyi entropy of a thermal mixed state of the doubled system. This mixed state incorporates three types of quantum statistical behavior: classically correlated, quantum entangled, and classically uncorrelated. We apply our prescription to 2D CFTs with Virasoro symmetry and recover the holographic dual formulation in terms of AdS3 gravity.

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