Vector meson propagator and baryon current conservation

Abstract

If baryons couple only with $\omega $-mesons, one found the baryon spectral function may be negative. We show this unacceptable result is caused by the $k_\mu k_\nu $-terms in the $\omega $-meson propagator. Their contribution may not vanish in approximate calculations which violate the baryon current conserves. A rule is suggested, by which the calculated baryon spectral function is well behaved.