Coupled Dyson-Schwinger Equations and Effects of Self-Consistency

Using the σ − ω model as an effective tool, the effects of selfconsistency are studied in some detail. A coupled set of DysonSchwinger equations for the renormalized baryon and meson propagators in the σ− ω model is solved self-consistently according to the dressed Hartree-Fock scheme, where the hadron propagators in both the baryon and meson self-energies are required to also satisfy this coupled set of equations. It is found that the self-consistency affects the baryon spectral function noticeably, if only the interaction with σ mesons is considered. However, there is a cancellation between the effects due to the σ and ω mesons and the additional contribution of ω mesons makes the above effect insignificant. In both the σ and σ − ω cases the effects of self-consistency on meson spectral function are perceptible, but they can nevertheless be taken account of without a self-consistent calculation. Our study indicates that to include the meson propagators in the self-consistency requirement is unnecessary and one can stop at an early step of an iteration procedure to obtain a good approximation to the fully self-consistent results of all the hadron propagators in the model, if an appropriate initial input is chosen. Vertex corrections and their effects on ghost poles are also studied. PACS :21. 60 Jz, 21. 65. +f, 11. 10. Gh.