This book presents the better understanding of infrared structures
of particle scattering processes in quantum electrodynamics (QED)
in four-dimensional spacetime. An S-matrix is the fundamental
quantity in scattering theory. However, if a theory involves
massless particles, such as QED and gravity, the conventional
S-matrix has not been well defined due to the infrared divergence,
and infrared dynamics thus needs to be understood in-depth to
figure out the S-matrix. The book begins with introducing
fundamental nature of the charge conservation law associated with
asymptotic symmetry, and explaining its relations to soft theorems
and memory effect. Subsequently it looks into an appropriate
asymptotic state of the S-matrix without infrared divergences. The
Faddeev-Kulish dressed state is known as a candidate of such a
state, and its gauge invariant condition and its relation to the
asymptotic symmetry are discussed. It offers an important building
blocks for constructing the S-matrix without infrared divergences.
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