非平衡态的有效场论：布朗量子场
Effective Field Theory out of Equilibrium: Brownian quantum fields
摘要：
本文研究了在有限温浴中，轻场--系统--与重场相互作用的情况下，有效场论脱离平衡的出现。我们得到了光场的约化密度矩阵，它的时间演化由包含重自由度关联的\emph{influence action}的有效作用量决定。非平衡态有效场论给出了光场的朗之万运动方程，该方程包含耗散核和噪声核，且服从广义涨落耗散关系。这些完全由浴的光谱密度确定，该光谱密度针对几种情况进行了详细分析。在$T=0$，我们阐明了重整化方面的阈值的效果和一个单一的时间演化的局部有效场论的渐近出现。在$T\neq 0$新的“异常”阈值出现，特别是\emph{decay}的环境重领域进入轻领域导致\emph{dissipative}动态的轻领域。即使当重浴颗粒被热抑制时，这种耗散贡献也导致光场的\emph{thermalization}，这通过量子动力学分析来证实。我们得到的量子主方程，并明确表明，它的解决方案，在外地的基础正是影响行动，决定了有效的非平衡场论。量子主方程的Lindblad形式以\emph{time dependent dissipative coefficients}为特征。它们的时间依赖性对于在渐近长时间下提取重正化效应是至关重要的。量子主方程的动力学与有效作用量、朗之万动力学和量子动力学的动力学完全一致，从而为有效场论的非平衡态研究提供了一个统一的框架。
英文摘要：
The emergence of an effective field theory out of equilibrium is studied in the case in which a light field --the system-- interacts with very heavy fields in a finite temperature bath. We obtain the reduced density matrix for the light field, its time evolution is determined by an effective action that includes the \emph{influence action} from correlations of the heavy degrees of freedom. The non-equilibrium effective field theory yields a Langevin equation of motion for the light field in terms of dissipative and noise kernels that obey a generalized fluctuation dissipation relation. These are completely determined by the spectral density of the bath which is analyzed in detail for several cases. At $T=0$ we elucidate the effect of thresholds in the renormalization aspects and the asymptotic emergence of a local effective field theory with unitary time evolution. At $T\neq 0$ new "anomalous" thresholds arise, in particular the \emph{decay} of the environmental heavy fields into the light field leads to \emph{dissipative} dynamics of the light field. Even when the heavy bath particles are thermally suppressed this dissipative contribution leads to the \emph{thermalization} of the light field which is confirmed by a quantum kinetics analysis. We obtain the quantum master equation and show explicitly that its solution in the field basis is precisely the influence action that determines the effective non-equilibrium field theory. The Lindblad form of the quantum master equation features \emph{time dependent dissipative coefficients}. Their time dependence is crucial to extract renormalization effects at asymptotically long time. The dynamics from the quantum master equation is in complete agreement with that of the effective action, Langevin dynamics and quantum kinetics, thus providing a unified framework to effective field theory out of equilibrium.
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