THERMO-FIELD DYNAMICS IN TIME REPRESENTATION

Making use of the thermo field dynamics (TFD) we formulate a calculabl e method for time-dependent nonequilibrium systems in a time represent ation (t-representation) rather than in the k0-Fourier representation. The corrected one-body propagator in the t-representation has the for m of B-1 (diagonal matrix) B (B being a thermal Bogoliubov matrix). Th e number parameter in B here is the observed number (the Heisenberg nu mber) with a fluctuation. With the usual definition of the on-shell se lf-energy a self-consistent renormalization condition leads to a kinet ic equation for the number parameter. This equation turns out to be th e Boltzmann equation, from which the entropy law follows.