  We study the properties of the $\Delta$ isobar in the symmetric and
asymmetric nuclear matter using the QCD sum rules approach based on the energy
dispersion relation. Allowing for different continuum thresholds for the
polarization tensors with different dimensions, we find stable masses for the
$\Delta$ in both the vacuum and the medium. Compared to the nucleon case, we
find that the vector repulsion is smaller for the $\Delta$ while the scalar
attraction is similar (75 MeV vector repulsion and 150 MeV scalar attraction in
the symmetric matter). The smaller vector repulsion can be understood using the
Pauli principle and a constituent quark model. Also the isospin dependence of
the quasiparticle energy, which mainly comes from the vector self energy, is
quite weak. We also allow for an explicit $\pi -N$ continuum contribution to
the polarization function, but find its effect to be minimal. Phenomenological
consequences of our results are discussed.
