Time-dependent canonical formalism of thermally dissipative fields and renormalization scheme

The canonical formalism of thermally dissipative semifree fields in the time-dependent situation is presented. The use of thermal covenant derivatives simplifies the formulation considerably. With this formalism one can unambiguously obtain the interaction Hamiltonian under any thermal situation which together with the free propagator enables perturbative calculations to be performed. The "on-shell" renormalization condition in the time-dependent case is also discussed. The model of a system with a thermal reservoir illustrates how the present formalism works in time-dependent situations.