论文标题
宇宙学空间上的空间功能重归其化组和哈达玛德态
The spatial Functional Renormalization Group and Hadamard states on cosmological spacetimes
论文作者
论文摘要
在全球双曲线空间（Lorentzian Signature）上引入了功能重归于（FRG）的空间变体（FRG）。通过其扰动扩张，人们认为这样的FRG必须不可避免地取决于状态，并且应该基于Hadamard状态。在Fliedmann-Lema-tre-tre空间上，提出了针对标量量子场的具体实现。 Hadamard状态的通用紫外线行为允许将流量与单环重新归一化的流动相匹配（在严格的去除紫外线截止的情况下，需要一个电势塔，一个用于RICCI标量的每个功率）。对于低能状态，研究了该流量的状态依赖性红外行为，在通货膨胀的时期内被认为是可行的真空。对于任何比例因子，都会出现一个简单的时间依赖性红外固定点方程（类似于Minkowski空间中的），并具有可分析的可计算校正来编码红外hadamard属性的非扰动分歧。
A spatial variant of the Functional Renormalization Group (FRG) is introduced on (Lorentzian signature) globally hyperbolic spacetimes. Through its perturbative expansion it is argued that such a FRG must inevitably be state dependent and that it should be based on a Hadamard state. A concrete implementation is presented for scalar quantum fields on flat Friedmann-Lemaître spacetimes. The universal ultraviolet behavior of Hadamard states allows the flow to be matched to the one-loop renormalized flow (where strict removal of the ultraviolet cutoff requires a tower of potentials, one for each power of the Ricci scalar). The state-dependent infrared behavior of the flow is investigated for States of Low Energy, which are Hadamard states deemed to be viable vacua for a pre-inflationary period. A simple time-dependent infrared fixed point equation (resembling that in Minkowski space) arises for any scale factor, with analytically computable corrections coding the non-perturbative ramifications of the Hadamard property in the infrared.
