Within the real-time formulation of non-equilibrium field theory generalized transport equations are derived avoiding the standard quasiparticle approximation. They permit to include unstable particles into the transport scheme. In order to achieve a self-consistent, conserving and thermodynamically consistent description, we generalize the Baym's Φ-functional method to genuine non-equilibrium processes. This scheme may be closed at any desired loop order of the diagrams of the functional Φ this way defining a consistent effective theory. By means of a first-order gradient approximation the corresponding Kadanoff-Baym equations are converted into a set of coupled equations. This set consists of a time-irreversible generalized kinetic equation for the slowly varying space-time part of the phase-space distributions and a retarded equation, which provides the fast micro-scale dynamics represented by the four-momentum part of the distributions. Thereby, no constraint to the mass shell of the particles is required any further and the corresponding spectral mass distributions are treated dynamically. The description naturally includes all those quantum features already inherent in the corresponding equilibrium limit (Matsubara formalism). Memory effects appearing in collision term diagrams of higher order are discussed. The variational properties of Φ-functional permit to derive a generalized expression for the non-equilibrium kinetic entropy flow, which includes corrections from fluctuations and mass width effects. In special cases an H-theorem can be demonstrated implying that the entropy can only increase with time. Memory effects in the kinetic terms provide corrections to the kinetic entropy flow that in equilibrium limit recover the famous bosonic type T 3 ln T correction to the specific heat of Fermi liquids like Helium-3.

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We investigate the symmetry properties for Baym's Φ-derivable schemes. We show that in general the solutions of the dynamical equations of motion, derived from approximations of the Φ-functional, do not fulfill the Ward-Takahashi identities of the symmetry of the underlying classical action, although the conservation laws for the expectation values of the corresponding Noether currents are fulfilled exactly for the approximation. Further we prove that one can define an effective action functional in terms of the self-consistent propagators which is invariant under the operation of the same symmetry group representation as the classical action. The requirements for this theorem to hold true are the same as for perturbative approximations: The symmetry has to be realized linearly on the fields and it must be free of anomalies, i.e., there should exist a symmetry conserving regularization scheme. In addition, if the theory is renormalizable in Dyson's narrow sense, it can be renormalized with counter terms which do not violate the symmetry.

The theoretical concepts for the renormalization of self-consistent Dyson resummations, deviced in the first paper of this series, are applied to first example cases for the φ 4 -theory. Besides the tadpole (Hartree) approximation as a novel part the numerical solutions are presented which includes the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or 2PI effective action concept.

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

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Within finite temperature field theory, we show that truncated nonperturbative self-consistent Dyson resummation schemes can be renormalized with local counterterms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym's ⌽-derivable concept. The scheme generates both the renormalized self-consistent equations of motion and the closed equations for the infinite set of counterterms. At the same time the corresponding two-particle irreducible generating functional and the thermodynamical potential can be renormalized, consistent with the equations of motion. This guarantees that the standard ⌽-derivable properties such as thermodynamic consistency and exact conservation laws hold also for the renormalized approximation schemes. The proof uses the techniques of Bogoliubov-Parasiuk-Hepp-Zimmermann renormalization to cope with the explicit and the hidden overlapping vacuum divergences.

It is shown that the Kadanoff-Baym equations at consistent first-order gradient approximation reveal exact rather than approximate conservation laws related to global symmetries of the system. The conserved currents and energy-momentum tensor coincide with corresponding Noether quantities in the local approximation. These exact conservations are valid, provided a Φ derivable approximation is used to describe the system, and possible memory effects in the collision term are also consistently evaluated up to first-order gradients.