论文标题
阈值和红外奇点：时间演变，渐近状态和纠缠熵
Threshold and infrared singularities: time evolution, asymptotic state and entanglement entropy
论文作者
论文摘要
在模型量子场理论中，研究了阈值和红外差异作为粒子产生的可能机制，并将其与通常从中获得概括的衰减过程进行了比较。衰减粒子传播器的光谱表示表明，衰减，阈值和红外奇异性，而看似不同的现象在质量上相关。我们实施一种非扰动动力重新召开方法来研究初始状态的时间演变。它显然是统一的，并产生渐近状态和产生的颗粒的分布功能。而衰减过程中的生存概率则以$ e^{ - γt} $下降，而对于阈值和红外发散案例，$ e^{ - \ sqrt { - \ sqrt {t/t/t^*}}} $分别分别与$ t^{ - δ} $，$ugγ，$umγ\ prop（coup） \ propto（耦合）^4 $。 Despite the different decay dynamics, the asymptotic state is qualitatively similar: a kinematically entangled state of the daughter particles with a distribution function which fulfills the unitarity condition and is strongly peaked at energy conserving transitions but broadened by the "lifetime" $1/Γ~;~ t^*$ for usual decay and threshold singularity, whereas it scales with the anomalous dimension $Δ$ for the红外奇异案例。阈值和红外不稳定性是生产机制与粒子衰减一样有效。如果其中一个粒子在黑暗部门而未观察到，则信息丢失会产生由分布函数确定的纠缠熵，并在单一时间演化时增加。
Threshold and infrared divergences are studied as possible mechanisms of particle production and compared to the usual decay process in a model quantum field theory from which generalizations are obtained. A spectral representation of the propagator of the decaying particle suggests that decay, threshold and infrared singularities while seemingly different phenomena are qualitatively related. We implement a non-perturbative dynamical resummation method to study the time evolution of an initial state. It is manifestly unitary and yields the asymptotic state and the distribution function of produced particles. Whereas the survival probability in a decay process falls off as $e^{-Γt}$, for threshold and infrared divergent cases falls off instead as $e^{-\sqrt{t/t^*}}$ and $t^{-Δ}$ respectively, with $Γ, Δ\propto (coupling)^2$ whereas $1/t^* \propto (coupling)^4$. Despite the different decay dynamics, the asymptotic state is qualitatively similar: a kinematically entangled state of the daughter particles with a distribution function which fulfills the unitarity condition and is strongly peaked at energy conserving transitions but broadened by the "lifetime" $1/Γ~;~ t^*$ for usual decay and threshold singularity, whereas it scales with the anomalous dimension $Δ$ for the infrared singular case. Threshold and infrared instabilities are production mechanisms just as efficient as particle decay. If one of the particles is in a dark sector and not observed, the loss of information yields an entanglement entropy determined by the distribution functions and increases upon unitary time evolution.
