The effective action approach applied to nuclear matter — I

Within the framework of the Walecka model (QHD-I) the application of the Cornwall-Jackiw-Tomboulis (CJT) effective action to nuclear matter is presented. The main feature is the treatment of the meson condensates for the system of finite nuclear density. The system of coupled Schwinger-Dyson (SD) equations is derived. It is shown that the SD equations for sigma-omega mixings are absent in this formalism. Instead, the energy density of the nuclear ground state does explicitly contain the contributions from the ring diagrams, amongst others. In the bare-vertex approximation, the expression for energy density is written down for numerical computation in the next paper.