Self-consistent structure in a relativistic Dirac-Hartree-Fock approximation

A self-consistent approximation structure is derived for the Dirac-Hartree-Fock (DHF) approximation in the σ-ω model of quantum hadrodynamics (QHD), by employing Landau's requirement for a quasiparticle energy in the self-consistent framework of the DHF approximation. The self-consistency condition for nuclear matter approximations, the Hugenholtz-Van Hove theorem, is applied to produce functional equations for self-energies, and solutions of the self-energies are obtained. The Hugenholtz-Van Hove theorem is satisfied exactly, and retardation effects in DHF approximation are self-consistently constructed to preserve the HV theorem. The present approximation is also discussed in terms of the theory of conserving approximations, which leads to the stationary condition of the variation of energy density with respect to self-energies. The present self-consistent calculations may support a theoretical approach to build a conserving structure in nonperturbative, self-consistent nuclear matter approximations