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arXiv 2007.02518hep-th
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装扮渐近态与QED红外物理

Dressed-Asymptotic States and QED Infrared Physics

Hideo Furugori, Shin'ichi Nojiri

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21 pages, two figure, title is changed, several revisions
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摘要：

在量子场论（QFT）中，将软粒子间的相互作用引入到渐近态中的缀饰态理论被认为是解决红外发散问题的有效方法。一个特别著名的例子是Kulish和Faddeev在量子电动力学（QED）中提出的修饰态形式主义。然而，正如Hirai和Sugishita所指出的，这种形式主义在规范不变性和IR发散方面存在问题。这些问题主要是由鬼模或非物理光子模的存在引起的。因此，我们从研究库仑规范中的渐近态开始，它不包括鬼和/或非物理光子模式。在本文中，我们提出了一种形式主义，直接从理论的相互作用，通过设置一个足够大的时间尺度$T$的渐近状态。在这个缀饰态形式中，我们用$1/T$的某个固定阶来定义在$|t|>T$上剩余的渐近相互作用，并且我们根据该阶来执行所有的计算。我们只研究量子电动力学中的渐近态，但我们可以将本文提出的缀饰态形式主义正式应用于任何微扰量子场论。我们证明，至少在QED中，我们可以用本文提出的修饰态构造无发散的酉$S$ -矩阵。此外，我们还讨论了跃迁率，表明我们可以预测实验结果。我们还证明了$S$ -矩阵的$\mathrm{U}(1)$规范对称性导致了QED大规范对称性，并且类空超曲面的矢势期望值的偏差表现为QED记忆效应.本文提出的缀饰态理论可以为研究红外物理提供一个统一的新视角，包括渐近对称性、记忆效应和态演化的么正性。

英文摘要：

The dressed state formalisms, which incorporate interactions of soft particles into an asymptotic state, are known as the prescriptions expected to solve the problem of infrared (IR) divergence in the quantum field theory (QFT). A particularly famous example is the dressed state formalism proposed by Kulish and Faddeev in quantum electrodynamics (QED). As pointed out by Hirai and Sugishita, however, this formalism has problems in gauge invariance and the IR divergence. These problems are mainly caused by the existence of ghosts or unphysical photon modes. Therefore, we start by studying the asymptotic states in the Coulomb gauge, which excludes ghosts and/or unphysical photon modes. In this paper, we propose a formalism to construct the asymptotic states directly from the interaction of the theory by setting a sufficiently large time scale $T$. In this dressed state formalism, we define the asymptotic interaction remaining at $|t|>T$ in terms of some fixed order of $1/T$, and we are performing all calculations according to that order. We study the asymptotic states in QED specifically, but we can formally apply the dressed state formalism proposed in this paper to any perturbative QFT. We show that, at least in QED, we can construct divergence-free and unitary $S$-matrix using dressed states proposed in this paper. Furthermore, we discuss the transition rate to show that we can predict experimental results. We also show that the $\mathrm{U}(1)$ gauge symmetry of $S$-matrix leads to the QED large gauge symmetry, and deviation of the expectation values of the vector potential between initial and final spacelike hypersurfaces emerges as a QED memory effect. The dressed state formalism in this paper may give a unified and new insight into IR physics, including asymptotic symmetries, memory effects, and unitarity of the state evolution.

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