  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.
