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Relativistic quantum field theories for complex scalar and Dirac fields areinvestigated in non-equilibrium thermo field dynamics. The thermal vacuum isdefined by the Bogoliubov transformed creation and annihilation operators. Twoindependent Bogoliubov parameters are introduced for a charged field. Itsdifference naturally induces the chemical potential. Time-dependent thermalBogoliubov transformation generates the thermal counter terms. We fix the termsby the self-consistency renormalization condition. Evaluating the thermalself-energy under the self-consistency renormalization condition, we derive thequantum Boltzmann equations for the relativistic fields.

Non-Equilibrium Thermo Field Dynamics for Relativistic Complex Scalar and Dirac Fields