Self-consistent approximations to non-equilibrium many-body theory

Abstract

Within the non-equilibrium Green's function technique on the real time contour, the Φ-functional method of Baym is reviewed and generalized to arbitrary nonequilibrium many-particle systems. The scheme may be closed at any desired order in the number of loops or vertices of the generating functional. It defines effective theories, which provide a closed set of coupled classical field and Dyson equations, which are self-consistent, conserving and thermodynamically consistent. The approach permits to include unstable particles and therefore unifies the description of resonances with all other particles, which obtain a mass width by collisions, decays or creation processes in dense matter. The inclusion of classical fields enables the treatment of soft modes and phase instabilities. The method can be taken as a starting point for adequate and consistent quantum improvements of the in-medium rates in transport theories.GSI-Preprint-98-34, subm. to Nucl. Phys. B

Range of validity of transport equations

“…However, if they are not applied then a gradient expansion would become too cumbersome to be of use in practical calculations. The derivation of transport equations has been discussed in great detail in the literature [14,15,16,17,18,19,20,21,22,23,24,25,26]. Most discussions focus on kinetic theory employing the additional approximation of a suitable quasi-particle ansatz, which goes beyond assumptions 1) -3).…”

All orders Boltzmann collision term from the multiple scattering expansion of the self-energy

“…Equations Eq. (23) and (56) are often used in various calculations such as in-medium particle property calculations [43,44,45,46,47,48,49] and MonteCarlo simulations of many-body systems; but, as far as we know, a systematic derivation has been lacking. Within our quasi-particle approximation, our result is valid for all orders of perturbation theory and any number of participating particles.…”

All orders Boltzmann collision term from the multiple scattering expansion of the self-energy

“…Since the Kadanoff-Baym equation has been much discussed in the literature (see for example [52,54,55,56] for some discussion in the context of 2PI effective action methods), we have little more to add to this point.…”