  We study the density-density response function of a collection of charged
massive Dirac particles and present analytical expressions for the dynamical
polarization function in one, two and three dimensions. The polarization
function is then used to find the dispersion of the plasmon modes, and
electrostatic screening of Coulomb interactions within the random phase
approximation. We find that for massive Dirac systems, the oscillating screened
potential decays as $r^{-1}$, $r^{-2}$ and $r^{-3}$ in one, two, and three
dimensions respectively. However for massless Dirac systems there is no
electrostatic screening or Friedel oscillation in one dimension, and the
oscillating screened potential decays as $r^{-3}$ and $r^{-4}$, in two and
three dimensions respectively. Our analytical results for the polarization
function will be useful for exploring the physics of massive and massless Dirac
materials in different experimental systems with varying dimensionality.
