Dynamical renormalization group approach to quantum kinetics in scalar andgauge theories - art. no. 065006

We derive quantum kinetic equations from a quantum field theory implementin g a diagrammatic perturbative expansion improved by a resummation via the d ynamical renormalization group. The method begins by obtaining the equation of motion of the distribution function in perturbation theory. The solutio n of this equation of motion reveals secular terms that grow in time; the d ynamical renormalization group resums these secular terms in real time and leads directly to the quantum kinetic equation. This method allows us to in clude consistently medium effects via resummations akin to hard thermal loo ps but away from equilibrium. A close relationship between this approach an d the renormalization group in Euclidean field theory is established In par ticular, coarse graining, stationary solutions, the relaxation time approxi mation, and relaxation rates have a natural parallel as irrelevant operator s, fixed points, linearization, and stability exponents in the Euclidean re normalization group, respectively. We used this method to study the relaxat ion in a cool gas of pions and sigma mesons in the O(4) chiral linear sigma model. We obtain in the relaxation time approximation the pion and sigma m eson relaxation rates. We also find that in the large momentum limit emissi on and absorption of massless pions result in a threshold infrared divergen ce in the sigma meson relaxation rate and lead to a crossover behavior in r elaxation. We then study the relaxation of charged quasiparticles in scalar quantum electrodynamics (SQED). We begin with a gauge invariant descriptio n of the distribution function and implement the hard thermal loop resummat ion for longitudinal and transverse photons as well as for the scalars. Whi le longitudinal, Debye-screened photons lead to purely exponential relaxati on, and transverse photons, only dynamically screened by Landau damping, le ad to anomalous (nonexponential) relaxation, thus leading to a crossover be tween two different relaxational regimes. We emphasize that infrared diverg ent damping rates are indicative of nonexponential relaxation and the dynam ical renormalization group reveals the correct relaxation directly in real time. Furthermore the relaxational time scales for charged quasiparticles a re similar to those found in QCD in a Self-consistent HTL resummation. Fina lly we also show that this method provides a natural framework to interpret and resolve the issue of pinch singularities out of equilibrium and establ ish a direct correspondence between pinch singularities and secular terms i n time-dependent perturbation theory. We argue that this method is particul arly well suited to study quantum kinetics and transport in gauge theories.