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 −α T t ln[t/t 0 ] for hard momentum charged excitations. This is in contrast with the usual quasiparticle interpretation of charged collective excitations at finite temperature in the sense of exponential relaxation of a narrow width resonance for which the width is the imaginary part of the self-energy on-shell. In the case of narrow resonances away from thresholds, this approach leads to the usual exponential relaxation. 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.12.38. Mh,11.15.Bt

Critical slowing down of the relaxation of the order parameter has phenomenological consequences in early universe cosmology and in ultrarelativistic heavy ion collisions. We study the relaxation rate of longwavelength fluctuations of the order parameter in an O(N) scalar theory near the critical point to model the non-equilibrium dynamics of critical fluctuations near the chiral phase transition. A lowest order perturbative calculation ͑two loops in the coupling ) reveals the breakdown of perturbation theory for long-wavelength fluctuations in the critical region and the emergence of a hierarchy of scales with hard qуT, semisoft Tӷq ӷT and soft Tӷq loop momenta which are widely separated in the weak coupling limit. A nonperturbative resummation is implemented to leading order in the large N limit which reveals the infrared renormalization of the static scattering amplitude and the crossover to an effective three dimensional theory for the soft loop momenta near the critical point. The effective three dimensional coupling is driven to the Wilson-Fisher three dimensional fixed point in the soft limit. This resummation provides an infrared screening and for critical fluctuations of the order parameter with wave vectors Tӷkӷk us or near the critical temperature Tӷm T ӷk us with the ultrasoft scale k us ϭ(T/4)exp͓Ϫ4/͔ the relaxation rate is dominated by classical semisoft loop momentum leading to ⌫(k,T)ϭT/(2N). For wave vectors kӶk us the damping rate is dominated by hard loop momenta and given by ⌫(k,T)ϭ4T/͓3N ln(T/k)͔. Analogously, for homogeneous fluctuations in the ultracritical region m T Ӷk us the damping rate is given by ⌫ 0 (m T ,T)ϭ4T/͓3N ln(T/m T )͔. Thus critical slowing down emerges for ultrasoft fluctuations. In such a regime the rate is independent of the coupling and both perturbation theory and the classical approximation within the large N limit break down. The strong coupling regime and the shortcomings of the quasiparticle interpretation are discussed.

We study the generation of magnetic fields during the stage of particle production resulting from spinodal instabilities during phase transitions out of equilibrium. The main premise is that long-wavelength instabilities that drive the phase transition lead to strong nonequilibrium charge and current fluctuations which generate electromagnetic fields. We present a formulation based on the nonequilibrium Schwinger-Dyson equations that leads to an exact expression for the spectrum of electromagnetic fields valid for general theories and cosmological backgrounds and whose main ingredient is the transverse photon polarization out of equilibrium. This formulation includes the dissipative effects of the conductivity in the medium. As a prelude to cosmology, we study magnetogenesis in Minkowski spacetime in a theory of N charged scalar fields to lowest order in the gauge coupling and to leading order in the large N within two scenarios of cosmological relevance. The long-wavelength power spectrum for electric and magnetic fields at the end of the phase transition is obtained explicitly. It follows that equipartition between electric and magnetic fields does not hold out of equilibrium. In the case of a transition from a high-temperature phase, the conductivity of the medium severely hinders the generation of magnetic fields; however, the magnetic fields generated are correlated on scales of the order of the domain size, which is much larger than the magnetic diffusion length. The implications of the results to cosmological phase transitions driven by spinodal instabilities are discussed.