Dressed-Asymptotic States and QED Large Gauge Symmetry
Hideo Furugori, Shin’ichi Nojiri · arXiv (Cornell University) · 2020
The dressed state formalisms are known as the prescriptions which are expected to solve the problem of infrared (IR) divergence in the quantum field theory. In the dressed state formalisms, we assume that there remain non-trivial interactions even in the far past or far future when the IR divergence exists, and the asymptotic states cannot be free particle states but the asymptotic states are dressed by an infinite number of soft particles. 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 study 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 finite time interval and analyzing the interactions that remain outside of the interval. In the formalism, some conditions imposed by Kulish and Faddeev are either unnecessary or naturally satisfied. In addition, we explicitly show that the $S$-matrix proposed in this paper is well-defined as a unitary matrix without any divergences, and we also discuss the physical transition rate to show that the dressed state formalism in this paper has predictability. Furthermore, we show that the degrees of freedom in the gauge transformations of the asymptotic states are related to the asymptotic symmetry of QED, which is called the large gauge symmetry. We also observe that functions of the large gauge transformation divide the Hilbert space to the super-selection sectors. ...