The theory of conserving approximations and the density functional theory in approximations for nuclear matter

Self-consistent relativistic approximations for nuclear matter are discussed in terms of the theory of conserving approximations and a self-consistent Green's function approach. Moreover, the nuclear density functional theory is explained in terms of the theory of conserving approximations. The analysis is applied to a relativistic field-theoretical model for nuclear matter, in order to construct self-consistent Dirac-Hartree-Fock and Dirac-Ring approximations that maintain the Hugenholtz-Van Hove theorem and Landau's hypothesis for quasiparticles. A self-consistent set of functional equations for self-energies is obtained by the stationary condition required by the theory of conserving approximations. The exact self-energy solutions are derived, and retardation corrections that maintain the Hugenholtz-Van Hove theorem and Landau's hypothesis for quasiparticle are generated explicitly in the self-energies. This approach is a direct method in order to construct self-consistent approximations for nuclear matter, and the results are applied to Fermi-liquid properties of nuclear matter and properties of neutron stars. (author)