Self-consistent approximations to non-equilibrium many-body theory Original Research Article

Within the non-equilibrium Green function technique on the real-time contour, the Φ-functional method of Baym is generalized to arbitrary non-equilibrium 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 one 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. Properties of resonances are discussed within the dilute density limit in terms of scattering phase shifts.