D. Boyanovsky, H.J. de Vega, and S.-Y. Wang
November 19, 1999
We derive quantum kinetic equations from a quantum field theory implementing a diagrammatic perturbative expansion improved by a resummation via the dynamical renormalization group. The method begins by obtaining the equation of motion of the distribution function in perturbation theory. The solution of this equation of motion reveals secular terms that grow in time, the dynamical renormalization group resums these secular terms in real time and leads directly to the quantum kinetic equation. This method allows to include consistently medium effects via resummations akin to hard thermal loops but away from equilibrium. A close relationship between this approach and the renormalization group in Euclidean field theory is established. In particular, coarse graining, stationary solutions, relaxation time approximation and relaxation rates have a natural parallel as irrelevant operators, fixed points, linearization and stability exponents in the Euclidean RG, respectively. We used this method to study the relaxation in a cool gas of resonances and pions in the O(4) chiral linear sigma model. We found that emission and absorption of massless pions results in threshold infrared divergences for large momentum of the resonance and leads to a crossover behavior in the relaxation. The relaxational and crossover time scales are discussed in detail. We then study the relaxation of charged quasiparticles in scalar QED. We begin with a gauge invariant description of the distribution function and implement the hard thermal loop resummation for longitudinal and transverse photons as well as for the scalars. While longitudinal, Debye screened photons lead to purely exponential relaxation, transverse photons, only dynamically screened by Landau damping lead to anomalous relaxation, thus leading to a crossover between two different relaxational regimes. We obtain the relaxational and crossover time scales as a function of momentum and argue that infrared divergent damping rates are indicative of non-exponential relaxation, the dynamical renormalization group reveals the correct relaxation directly in real time. Furthermore the relaxational time scales are similar to those found for QCD in a self-consistent HTL resummation. Finally we also show that this method provides a natural framework to interpret and resolve the issue of pinch singularities out of equilibrium and establish a direct correspondence between pinch singularities and secular terms in time dependent perturbation theory. We argue that this method is particularly well suited to study quantum kinetics and transport in gauge theories.
Department of Physics and Astronomy, University of
Pittsburgh, Pittsburgh, PA. 15260, U.S.A.
LPTHE, Université Pierre et Marie Curie (Paris VI) et Denis Diderot (Paris VII), Tour 16, 1er. étage, 4, Place Jussieu, 75252 Paris, Cedex 05, France