Understanding the entanglement of radiation in quantum field theory has been a long-standing challenge, with implications ranging from black hole thermodynamics to quantum information. We demonstrate how the case of the free fermion in $1+1$ dimensions reveals the details of the density matrix of the radiation produced by a moving mirror. Using the resolvent method rather than standard conformal field theory techniques we derive the Rényi entropies, modular Hamiltonian, and flow of the radiation and determine when mirrors generate unitary transformations.

中文翻译：

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AdS2 中的移动镜像、页面曲线和体熵

理解量子场论中的辐射纠缠一直是一项长期挑战，其影响范围从黑洞热力学到量子信息。我们演示了自由费米子的情况如何$1+1$维度揭示了移动镜产生的辐射密度矩阵的细节。使用解析方法而不是标准的共形场论技术，我们推导出 Rényi 熵、模哈密顿量和辐射流，并确定反射镜何时产生幺正变换。