  We study real-time correlation functions in scalar quantum field theories at
temperature $T=1/\beta$. We show that the behaviour of soft, long wavelength
modes is determined by classical statistical field theory. The loss of quantum
coherence is due to interactions with the soft modes of the thermal bath. The
soft modes are separated from the hard modes by an infrared cutoff $\L \ll
1/(\hbar\beta)$. Integrating out the hard modes yields an effective theory for
the soft modes. The infrared cutoff $\L$ controls corrections to the classical
limit which are $\cO{\hbar\beta\L}$. As an application, the plasmon damping
rate is calculated.
