  We introduce the method of dynamical renormalization group to study
relaxation and damping out of equilibrium directly in real time and applied it
to the study of infrared divergences in scalar QED. This method allows a
consistent resummation of infrared effects associated with the exchange of
quasistatic transverse photons and leads to anomalous logarithmic relaxation of
the form $e^{-\alpha T t \ln[t/t_0]}$ which prevents a quasiparticle
interpretation of charged collective excitations at finite temperature. The
hard thermal loop resummation program is incorporated consistently into the
dynamical renormalization group yielding a picture of relaxation and damping
phenomena in a plasma in real time that trascends the conceptual limitations of
the quasiparticle picture and other type of resummation schemes. We derive a
simple criterion for establishing the validity of the quasiparticle picture to
lowest order.
