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A relativistic neutral scalar field is investigated in non-equilibrium thermofield dynamics. The canonical quantization is applied to the fields out ofequilibrium. Because the thermal Bogoliubov transformation becomestime-dependent, the equations of motion for the ordinary unperturbed creationand annihilation operators are modified. This forces us to introduce a thermalcounter term in the interaction Hamiltonian which generates additionalradiative corrections. Imposing the self-consistency renormalization conditionon the total radiative corrections, we obtain the quantum Boltzmann equationfor the relativistic scalar field.

Canonical Quantization for a Relativistic Neutral Scalar Field in Non-equilibrium Thermo Field Dynamics