The self-consistent relativistic Fermi-sea particle formalism in the quantum hadrodynamics is discussed in terms of properties of conserving approximations. The relativistic Dirac-Hartree-Fock approximation (σ, ω, ρ, and π), for example, is examined from the point of view of the Hugenholtz–Van-Hove theorem and thermodynamics as a check for internal consistency. These two conditions sufficient for constructing conserving approximations are strict constraints on modification and simplification of the Fermi-sea particle approximations and should be used in order to define consistent quasiparticle approximations. It is shown that the pion vertex and retardation which enters through exchange corrections prevent conserving properties to be maintained in the Dirac-Hartree-Fock approximation, and this suggests a careful analysis of self-consistency in the relativistic formalism when correlation effects are considered. The relativistic Fermi-sea particle approximations can be defined uniquely when both constraints are incorporated into self-consistency of the approximations.

• Received 1 September 1989

DOI:https://doi.org/10.1103/PhysRevC.41.744