Quantization of the linearized Einstein–Klein–Gordon system on arbitrary backgrounds and the special case of perturbations in inflation
Quantization of the linearized Einstein–Klein–Gordon system on arbitrary backgrounds and the special case of perturbations in inflation
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DOI：
10.1088/0264-9381/31/21/215004
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发表时间：
2014-03
影响因子：
3.5
通讯作者：
Thomas-Paul Hack
中科院分区：
文献类型：
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作者：
Thomas-Paul Hack
我们以明显的协变和规范不变的方式将线性化的Einstein-Klein-Gordon系统映射到任意的壳层背景上。对于暴胀微扰的特殊情况，即Friedmann-Lemaitre-Robertson-步行者型壳层背景，我们将我们的一般量子化构造与暴胀微扰量子理论的标准方法进行了比较.我们发现，并不是所有的局部量子观测量的线性化Einstein-Klein-Gordon系统可以分为局部观测量的标量和张量类型的标准方法。然而，我们认为，这个子类的观测量是足够的测量扰动消失在空间无穷大，这是符合标准的假设。最后，我们评论最近的一个观察，在标准量子化，量子的Barbarian电位显示非本地的行为，并认为类似的现象发生在任何本地量子场论。作者希望，目前的工作可能构成一个桥梁之间的普遍适用，因此强大的框架代数量子场论弯曲时空和标准处理的扰动通货膨胀。
We quantize the linearized Einstein–Klein–Gordon system on arbitrary on-shell backgrounds in a manifestly covariant and gauge-invariant manner. For the special case of perturbations in inflation, i.e. on-shell backgrounds of Friedmann–Lemaître–Robertson–Walker type, we compare our general quantization construction with the standard approach to the quantum theory of perturbations in inflation. We find that not all local quantum observables of the linearized Einstein–Klein–Gordon system can be split into local observables of scalar and tensor type as in the standard approach. However, we argue that this subclass of observables is sufficient for measuring perturbations that vanish at spatial infinity, which is in line with standard assumptions. Finally, we comment on a recent observation that, upon standard quantization, the quantum Bardeen potentials display a non-local behaviour and argue that a similar phenomenon occurs in any local quantum field theory. It is the hope of the author that the present work may constitute a bridge between the generally applicable and thus powerful framework of algebraic quantum field theory in curved spacetimes and the standard treatment of perturbations in inflation.