H.J. de Vega,
and
S.-Y. Wang
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