A covariant generalization of the real-time Green's functions method in the theory of kinetic equations

A generalized quantum relativistic kinetic equation (RKE) of the Kadanoff-B aym type is obtained on the basis of the Heisenberg equations of motion whe re the time evolution and space translation are separated From each other b y means of the covariant method. The same approach is used also for a covar iant modification of the real-time Green's Functions method based on the Wi gner representation. The suggested approach does not contain arbitrariness' elements and uncertainties which often arise from derivation of RKE on the basis of the motion equations of the Kadanoff-Baym type for the correlatio n functions in the case of systems with inner degrees of freedom. Possibili ties of the proposed method are demonstrated by examples of derivation of R KE of the Vlasov type and collision integrals of the Boltzmann-Uehling-Uhie nbeck (BUU) type in the Frame of the oo-version of quantum hadrodynamics, f or the simplest case of spin saturated nuclear matter without antinuclear c omponent. Here. the quasiparticle approximation in a covariant performance is used. A generalization of the method for the description of strong non-e quilibrium slates based on the non-equilibrium statistical operator is then proposed as well. (C) 1999 Academic Press.