Canonical Quantization for a Relativistic Neutral Scalar Field in   Non-equilibrium Thermo Field Dynamics
  A relativistic neutral scalar field is investigated in non-equilibrium thermo field dynamics. The canonical quantization is applied to the fields out of equilibrium. Because the thermal Bogoliubov transformation becomes time-dependent, the equations of motion for the ordinary unperturbed creation and annihilation operators are modified. This forces us to introduce a thermal counter term in the interaction Hamiltonian which generates additional radiative corrections. Imposing the self-consistency renormalization condition on the total radiative corrections, we obtain the quantum Boltzmann equation for the relativistic scalar field. 
Yuichi Mizutani, Tomohiro Inagaki, Yusuke Nakamura and Yoshiya   Yamanaka
hep-th