  Sum rules for the variation of finite-density spectral density of vector
channel with baryon density are derived based on dispersion relations and the
operator product expansion. These sum rules may serve as constraints on the
phenomenological models for the finite-density spectral densities used in the
approaches motivated from QCD. Applying these sum rules to the rho meson in
nuclear medium with a simple pole-plus-continuum ansatz for the spectral
densities, we found that the qualitative features of the QCD sum-rule
predictions for the spectral parameters are consistent with these sum rules;
however, the quantitative QCD sum-rule results violate the sum rules to certain
degree.
