Coupled Dyson-Schwinger equations and effects of self-consistency

Using the sigma-omega model as an effective tool, the effects of self-consi stency are studied in some detail. A coupled set of Dyson-Schwinger equatio ns for the renormalized baryon and meson propagators in the sigma-omega mod el is solved self-consistently according to the dressed Hartree-Fock scheme , where the hadron propagators in both the baryon and meson self-energies a re required to also satisfy this coupled set of equations. It is found that the self-consistency affects the baryon spectral function noticeably, if o nly the interaction with sigma mesons is considered. However, there is a ca ncellation between the effects due to the sigma and omega mesons and the ad ditional contribution of co mesons makes the above effect insignificant. In both the a and sigma-omega cases the effects of self-consistency on meson spectral function are perceptible, but they can nevertheless be taken accou nt of without a self-consistent calculation. Our study indicates that to in clude the meson propagators in the self-consistency requirement is unnecess ary 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. (C) 2001 El sevier Science B.V. All rights reserved.