论文标题
弯曲的空间中的局部非相关量子系统：粒子探测器模型的一般表征
Localized non-relativistic quantum systems in curved spacetimes: a general characterization of particle detector models
论文作者
论文摘要
在本手稿中，我们提供了一种一致的方法，可以描述在背景弯曲时空中经历时间轨迹的局部非偏见量子系统。也就是说，使用费米正常坐标，我们确定了内部产品以及在轨迹的休息空间中定义的每个值适当时间的均值和动量运算符。然后，该框架自然提供了一个配方，用于将在非相关背景中定义的量子理论映射到围绕弯曲空间中的时光轨迹的理论中定义的量子理论。这是通过重新解释位置和动量运算符，并通过将局部红移因子引入汉密尔顿人来完成，这由于时空的曲率和轨迹的加速而产生了新的动力学。然后，我们将形式主义应用于粒子探测器模型，也就是说，在弯曲背景下非相关量子系统耦合到量子场的情况。这使人们可以为粒子探测器模型编写一般定义，该定义能够恢复文献中的先前模型。我们的框架还允许人们估计这些模型的有效性状态，表征了可以使用粒子探测器准确探测量子场的情况。
In this manuscript we provide a consistent way of describing a localized non-relativistic quantum system undergoing a timelike trajectory in a background curved spacetime. Namely, using Fermi normal coordinates, we identify an inner product and canonically conjugate position and momentum operators defined in the rest space of the trajectory for each value of its proper time. This framework then naturally provides a recipe for mapping a quantum theory defined in a non-relativistic background to a theory around a timelike trajectory in curved spacetimes. This is done by reinterpreting the position and momentum operators and by introducing a local redshift factor to the Hamiltonian, which gives rise to new dynamics due to the curvature of spacetime and the acceleration of the trajectory. We then apply our formalism to particle detector models, that is, to the case where the non-relativistic quantum system is coupled to a quantum field in a curved background. This allows one to write a general definition for particle detector models which is able to recover the previous models in the literature. Our framework also allows one to estimate the regime of validity of these models, characterizing the situations where particle detectors can be used to accurately probe quantum fields.
