Dressed-Asymptotic States From S-matrix and QED Large Gauge Symmetry

In order to solve the problem of the infrared (IR) divergence in the quantum field theory, the formalism proposed by Kulish and Faddeev (KF) is well-known. In the formalism, when the IR divergences appear, there remains non-trivial interaction even in the infinitely far past and future, and the asymptotic states cannot be the free particle states but the asymptotic states are dressed by infinite numbers of soft particles. Although the KF formalism is based on the Schr\"odinger picture, we construct the asymptotic states by using S-matrix keeping the asymptotic interaction that remains in far past and future as in the KF formalism. As a result, some conditions imposed by Kulish and Faddeev become unnecessary or naturally appear in our formulation. Furthermore, our asymptotic states satisfy the conditions for the gauge invariance proposed by Hirai and Sugishita based on the BRS symmetry. We also explicitly show that the IR divergences in the S-matrix of the quantum electrodynamics can be removed by using our formulation and clarify that the degrees of freedom in the gauge transformation of the asymptotic states are related to the asymptotic symmetry of the $S$-matrix. Therefore, the construction of the asymptotic states and the S-matrix in our formulation may give a new insight into the IR physics in various kinds of theories.