标题： 量子宇宙学时空中的大模度量出现 显示英文标题

标题： Metric emerging to massive modes in quantum cosmological space-times

摘要： 我们考虑一个质量较大的量子 Klein-Gordon 场探测一个各向同性的量子宇宙时空背景。 得到的结果令人惊讶。 事实证明，尽管量子引力场具有各向同性，但由 Klein-Gordon (K-G) 场的模式所经历的半经典度规是非各向同性的。 这种各向异性依赖于模式动量的方向。 具体来说，我们的工作是从场的一个模式出发推导出一个半经典的时空。 这种方法可以看作是在量子背景上的量子场论 (QFT) 和经典弯曲时空上的量子场论之间的比较，从而产生一个涌现的度规张量。 半经典度规张量的分量从量子 Klein-Gordon 场的传播方程计算得出，采用的是测试场近似。 这些各向异性本质上是量子的：它们与普朗克常数成正比，并“修饰”了经典极限下获得的各向同性经典时空。 显示英文摘要

摘要： We consider a massive quantum test Klein-Gordon field probing an isotropic quantum cosmological space-time in the background. The result obtained is surprising. It turns out, that despite the isotropy of the quantum gravitational field, the semi-classical metric experienced by a mode of the K-G field is non-isotropic. The anisotropy depends on the direction of the momentum of the mode. Specifically, what we do is to derive a semi-classical space-time which emerges to a mode of the field. The method amounts to a comparison between QFT on a quantum background and QFT on a classical curved space-time, giving rise to an emergent metric tensor. The components of the semi-classical metric tensor are calculated from the equation of propagation of the quantum K-G field in the test field approximation. The anisotropies are of a quantum nature: they are proportional to Planck constant and "dress" the isotropic classical space-time obtained in the classical limit.