  The problem of infrared divergence of the effective electromagnetic field
produced by elementary charges is revisited using the model of an electron
freely evolving in a photon bath. It is shown that for any finite travel time,
the effective field of the electron is infrared-finite, and that in each order
of perturbation theory the radiative contributions grow without bound in the
large-time limit. Using the Schwinger-Keldysh formalism, factorization of
divergent contributions in multi-loop diagrams is proved, and summation of the
resulting infinite series is performed. It is demonstrated that the effective
electromagnetic field of the electron vanishes in the large-time limit, and
that this vanishing respects the total charge conservation and the Gauss law.
It is concluded that the physical meaning of infrared singularity in the
effective field is the existence of a peculiar irreversible spreading of
electric charges, caused by their interaction with the photon field. This
spreading exists in vacuum as well as at finite temperature, and shows itself
in a damping of the off-diagonal elements of the momentum-space density matrix
of electron, but does not affect its momentum probability distribution. It
precludes preparation of spatially localized particle states at finite times by
operating with free particle states in the remote past. Relationship of the
obtained results to the Bloch-Nordsieck theorem is established, and discussed
from the standpoint of measurability of the electromagnetic field. The effect
of irreversible spreading on the electron diffraction in the classic two-slit
experiment is determined, and is shown to be detectable in principle by modern
devices already at room temperature.
