Meson Dynamics and the Nuclear Many-Body Problem. I. The Free-Nucleon Problem

Relativistic nucleon-meson field theory is cast in a form appropriate to the nuclear many-body problem. Martin-Schwinger thermodynamic Green's functions are employed. The $n$-nucleon Green's functions satisfy a set of coupled equations which is formally identical to those of the usual potential many-body problem. Here, however, the two-body potential is replaced by a time-dependent interaction in which the mesons are formally eliminated in favor of higher-order nucleon correlations. A general program of increasing complexity for obtaining approximate solutions to the equations is discussed. It is necessary to solve the "vacuum" (one-, two-, etc., nucleon propagator) first. This has been done in the "Hartree-Fock" approximation which sums all diagrams containing a single continuous nucleon line with all possible uncrossed $\pi$ and $\omega$ meson lines. Peaks in the spectral function are identified with masses of known $N^{*}$ resonances. The appearance of ghost states, which arise in the process of mass and wave-function renormalization, is discussed. The resultant Green's function is used to calculate the magnetic moment of the nucleon, yielding a significantly better isovector component of the magnetic moment than the usual perturbation theory, although the isoscalar component is poor in both cases.