Effects on the hadron propagators due to $k_\mu k_\nu $ terms in the vector meson propagator

In an approximation where the baryon current conservation is violated, the contribution of the $k_\mu k_\nu$ terms in the vector meson propagator may not vanish. Their effects on the baryon and meson spectral functions and on the consequences of self-consistency are studied in the relativistic self-consistent Hartree-Fock approximation by means of the $\sigma -\omega$ model. Two cases where the $k_\mu k_\nu$ terms are and are not neglected are compared. It is found that there is a marked change in the baryon spectral function which becomes more peaked in the latter case. Such a change remains even by a proper readjustment of parameters. The effects of self-consistency in the $\sigma -\omega$ model are qualitatively the same in both cases, though quantitatively there is some significant difference.