  Using the real time formalism of field theory at finite temperature and
density we have evaluated the in-medium $\omega$ self-energy from baryon and
meson loops. We have analyzed in detail the discontinuities across the branch
cuts of the self-energy function and obtained the imaginary part from the
non-vanishing contributions in the cut regions. An extensive set of resonances
have been considered in the baryon loops. Adding the meson loop contribution we
obtain the full modified spectral function of $\omega$ in a thermal gas of
mesons, baryons and anti-baryons in equilibrium for several values of
temperature and baryon chemical potential.
