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We introduce the method of dynamical renormalization group to studyrelaxation and damping out of equilibrium directly in real time and applied itto the study of infrared divergences in scalar QED. This method allows aconsistent resummation of infrared effects associated with the exchange ofquasistatic transverse photons and leads to anomalous logarithmic relaxation ofthe form $e^{-\alpha T t \ln[t/t_0]}$ which prevents a quasiparticleinterpretation of charged collective excitations at finite temperature. Thehard thermal loop resummation program is incorporated consistently into thedynamical renormalization group yielding a picture of relaxation and dampingphenomena in a plasma in real time that trascends the conceptual limitations ofthe quasiparticle picture and other type of resummation schemes. We derive asimple criterion for establishing the validity of the quasiparticle picture tolowest order.Comment: REVTEX, 33 pages, 2 figures,improved discussion,more examples,same  physics to appear in phys. rev.

Dynamical renormalization group resummation of finite temperature infrared divergences