Classical fields as coherent states and diffusion equations
  We present a derivation of the effect of the classical field configuration to the diffusion equations. Using the formalism of the thermo field dynamics we propose a systematic and consistent way to treat the classical background and to calculate it's effect at any order of the perturbation theory. We treat the classical field in genuine quantum field theory formalism as a coherent state and show how the propagators and self energies are altered in this case. 
Jukka Sirkka and Iiro Vilja