The critical density of neutral pion condensation is reinvestigated based on the relativistic framework and compared with nonrelativistic results. The particle-hole and delta-hole polarizations of the pion selfenergy are calculated in the relativistic way by using a new set of Landau–Migdal parameters derived from recent experimental data. It is concluded that the use of relativistic particle-hole and delta-hole excitations for the pion selfenergy increases the critical density, but still leads to condensation for densities from two to three times the normal nuclear matter density within the random phase approximation.

The role of effective hadron masses and effective couplings in nuclear matter is studied using a generalized effective Lagrangian for σ-ω model. A simple relation among the effective masses, the effective couplings and the incompressibility K is derived. Using the relation, it is found that the effective repulsive and the effective attractive forces are almost canceled to each other at the normal density. Inversely, if this cancellation is almost complete, K should be 250∼350MeV.

Relations among effective hadron masses, effective interactions and equations of state are studied using a generalized mean-field theory that includes the implicit and explicit density dependence of the effective masses and couplings. We find that we can make the effective ω-meson mass smaller and the equation of state softer simultaneously if the ω-meson mean field is proportional to the baryon density. In this case, there is a simple and exact relation between the effective ω-meson mass and the effective ω-nucleon coupling. According to this relation, the effective ω-nucleon coupling automatically decreases if the effective ωmeson mass decreases. Consequently, the equation of state becomes softer. An attempt to incorporate the QCD sum-rule results into the hadron field theory is also made.

Using the generalized mean field theory, we have studied the relation among the effective meson masses, the effective meson-nucleon couplings and the equation of state (EOS) in asymmetric nuclear matter. If the effective ωmeson mass becomes smaller at high density, the EOS becomes stiffer. However, if we require that the ω-meson mean field is proportional to the baryon density, the effective ω-nucleon coupling automatically becomes smaller at the same time as the effective ω-meson mass becomes smaller. Consequently, the EOS becomes softer. A similar relation is found for the effective ρ-meson mass and the effective ρ-nucleon coupling. We have also studied the relation among the effective meson masses, the effective meson-nucleon couplings and a radius R of a neutron star. The R depends somewhat on the value of the effective ω-meson mass and the effective ω-nucleon coupling. The ambiguity of R is a few hundred meters if |m * ω0 2 − m 2 ω | ∼ 0.1m 2 ω at the normal density.

We develop the Nuclear Schwinger–Dyson (NSD) formalism to include the effects of ladder diagrams by modifying the vertex. In this extension, the NSD equation sums up both ring diagrams and ladder diagrams self-consistently. The results are compared with mean field theory, Hartree Fock and bare-vertex NSD calculations. It is shown that the vertex correction is important from the following viewpoints. First, the vertex correction greatly modifies the meson propagators, and we can avoid the ghost-pole from meson propagators in a self-consistent way. Secondly, it gives a large negative correlation-energy compared with the other calculations; as a result, it gives a softer equation of state which is preferable according to the experimental data.