  We study the kinetics of the distribution function for charged particles of
hard momentum in scalar QED. The goal is to understand the effects of infrared
divergences associated with the exchange of quasistatic magnetic photons in the
relaxation of the distribution function. We begin by obtaining a kinetic
transport equation for the distribution function for hard charged scalars in a
perturbative expansion that includes hard thermal loop resummation. Solving
this transport equation, the infrared divergences arising from absorption and
emission of soft quasi-static magnetic photons are manifest in logarithmic
secular terms. We then implement the dynamical renormalization group
resummation of these secular terms in the relaxation time approximation. The
distribution function (in the linearized regime) is found to approach
equilibrium as $\delta n_k(t) =\delta n_k(t_o) e^{-2\alpha T (t-t_o)
\ln[(t-t_o)\bar{\mu}]}$, with $\bar{\mu}\approx \omega_p$ the plasma frequency
and $\alpha =e^2/4\pi$. This anomalous relaxation is recognized to be the
square of the relaxation of the single particle propagator, providing a
generalization of the usual relation between the damping and the interaction
rate. The renormalization group approach to kinetics reveals clearly the time
scale $t_{rel} \approx (\alpha T \ln[1/\alpha])^{-1}$ arising from infrared
physics and hinges upon the separation of scales $t_{rel} >>\omega_p^{-1}$.
