NUCLEAR SCHWINGER-DYSON FORMALISM APPLIED TO FINITE BARYON DENSITY .1. FORMULATION

The nuclear Schwinger-Dyson (NSD) formalism is presented for an applic ation to nuclear matter. The NSD formalism consists of coupled Dyson e quations of a nucleon and mesons. Because it includes meson self-energ ies in a nonperturbative way, higher-order correlations beyond the Har tree-Fock approximation are taken into account. Some important differe nces between the NSD formalism for the system of finite baryon density and SD formalism of zero baryon density are shown. The main differenc e is due to the existence of condensed meson fields. By paying special attention to the treating of the condensed meson fields, the coupled Dyson equations of nucleon and mesons are derived based on a functiona l method. It is shown that this treating of the condensed fields natur ally leads to two-tadpole energy, which cancels a half of the Hartree energy. A general representation of vector meson propagators is derive d by using projection operators and by solving an inverse matrix probl em. It is also shown that the NSD method is possible to be generalized to include sigma-omega meson mixings and new coupled meson propagator s are obtained in a similar way to the nonmixed case. As a result, 5x5 components of the coupled meson propagator are expressed in terms of only four independent propagators. By using these meson propagators, e xplicit expressions of NSD coupled equations and the energy density of nuclear matter are derived for numerical calculations in a subsequent paper. Similarities and differences between NSD and traditional metho ds such as the mean-field theory or Hartree-Fock are discussed.