Dressed asymptotic states and QED infrared physics,Physical Review D

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Dressed asymptotic states and QED infrared physics
Physical Review D ( IF 4.6 ) Pub Date : 2021-12-03 , DOI: 10.1103/physrevd.104.125004
Hideo Furugori (古郡秀雄) ₁ , Shin’ichi Nojiri _{1,

2}

Affiliation

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 timescale

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 a 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 U(1) gauge symmetry of the

S

-matrix leads to the QED large gauge symmetry, and the 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.

中文翻译：

装扮渐近态和 QED 红外物理

将软粒子的相互作用纳入渐近态的修饰态形式被称为有望解决量子场论 (QFT) 中红外 (IR) 发散问题的处方。一个特别著名的例子是 Kulish 和 Faddeev 在量子电动力学 (QED) 中提出的装饰态形式主义。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 散度方面存在问题。这些问题主要是由鬼影或非物理光子模式的存在引起的。因此，我们首先研究库仑规范中的渐近态，其中不包括重影和/或非物理光子模式。在本文中，我们提出了一种形式主义，通过设置足够大的时间尺度，直接从理论的相互作用中构建渐近状态