Classical limit for scalar fields at high temperature Original Research Article

We study real-time correlation functions in scalar quantum field theories at temperature T = 1/β. We show that the behaviour of soft, long-wave-length 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 Λ ⪡ 1/(h̷β). Integrating out the hard modes yields an effective theory for the soft modes. The infrared cutoff Λ controls corrections to the classical limit which are O(ħβΛ). As an application, the plasmon damping rate is calculated.