  The effect of electron-electron scattering on the equilibrium properties of
few-electron quantum dots is investigated by means of nonequilibrium Green's
functions theory. The ground and equilibrium state is self-consistently
computed from the Matsubara (imaginary time) Green's function for the spatially
inhomogeneous quantum dot system whose constituent charge carriers are treated
as spin-polarized. To include correlations, the Dyson equation is solved,
starting from a Hartree-Fock reference state, within a conserving (second
order) self-energy approximation where direct and exchange contributions to the
electron-electron interaction are included on the same footing.
  We present results for the zero and finite temperature charge carrier
density, the orbital-resolved distribution functions and the self-consistent
total energies and spectral functions for isotropic, two-dimensional parabolic
confinement as well as for the limit of large anisotropy--quasi-one-dimensional
entrapment. For the considered quantum dots with N=2, 3 and 6 electrons, the
analysis comprises the crossover from Fermi gas/liquid (at large carrier
density) to Wigner molecule or crystal behavior (in the low-density limit).
