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arXiv 2201.04701hep-phhep-thquant-ph
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阈值和红外奇异性：时间演化、渐近态和纠缠熵

Threshold and infrared singularities: time evolution, asymptotic state and entanglement entropy

Daniel Boyanovsky

备注：
published version
发表信息：
Phys. Rev. D 105, 056012 (2022)
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摘要：

阈值和红外发散粒子生产的可能机制进行了研究，并在一个模型量子场论，从中得到概括的通常的衰变过程相比。衰变粒子的传播子的光谱表示表明，衰变，阈值和红外奇异性，而看似不同的现象是定性相关的。我们实现了一种非微扰动力学重算方法来研究初始状态的时间演化。它显然是酉的，并给出了所产生粒子的渐近状态和分布函数。而在衰减过程中的生存概率下降为$e^{-Γt}$，对于阈值和红外发散情况，分别下降为$e^{-\sqrt{t/t^*}}$和$t^{-Δ}$，其中$Γ, Δ\propto (coupling)^2$而$1/t^* \propto (coupling)^4$。尽管不同的衰变动力学，渐近状态是定性相似的：一个运动学纠缠态的子粒子的分布函数，满足么正性条件，并强烈达到峰值，在能量守恒的过渡，但扩大了“寿命”$1/Γ~;~ t^*$通常的衰变和阈值奇异性，而它的规模与异常尺寸$Δ$的红外奇异情况。阈值和红外不稳定性是与粒子衰变一样有效的产生机制。如果其中一个粒子处于暗区而未被观测到，信息的丢失会产生由分布函数决定的纠缠熵，并在幺正时间演化时增加。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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