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We derive quantum kinetic equations from a quantum field theory implementinga diagrammatic perturbative expansion improved by a resummation via thedynamical renormalization group. The method begins by obtaining the equation ofmotion of the distribution function in perturbation theory. The solution ofthis equation of motion reveals secular terms that grow in time, the dynamicalrenormalization group resums these secular terms in real time and leadsdirectly to the quantum kinetic equation. We used this method to study therelaxation in a cool gas of pions and sigma mesons in the O(4) chiral linearsigma model. We obtain in relaxation time approximation the pion and sigmameson relaxation rates. We also find that in large momentum limit emission andabsorption of massless pions result in threshold infrared divergence in sigmameson relaxation rate and lead to a crossover behavior in relaxation. We thenstudy the relaxation of charged quasiparticles in scalar electrodynamics(SQED). While longitudinal, Debye screened photons lead to purely exponentialrelaxation, transverse photons, only dynamically screened by Landau dampinglead to anomalous relaxation, thus leading to a crossover between two differentrelaxational regimes. We emphasize that infrared divergent damping rates areindicative of non-exponential relaxation and the dynamical renormalizationgroup reveals the correct relaxation directly in real time. Finally we alsoshow that this method provides a natural framework to interpret and resolve theissue of pinch singularities out of equilibrium and establish a directcorrespondence between pinch singularities and secular terms. We argue thatthis method is particularly well suited to study quantum kinetics and transportin gauge theories.Comment: RevTeX, 40 pages, 4 eps figures, published versio

Dynamical renormalization group approach to quantum kinetics in scalar and gauge theories