EXACT DIAGONALIZATION OF THE INTERACTING PROPAGATOR FOR THE 2D ELECTRON-GAS IN A MAGNETIC-FIELD

The spatial dependence of the exact one electron propagator for an interacting 2D electron gas in a magnetic field is shown to be the same as for a non-interacting gas. This happens whenever the translational symmetry is unbroken in the ground state. The result may be extended to a more general class of systems. The translational symmetry also implies that the density of states has the same kind of discrete character as in the non-interacting case. This is shown explicitly in the Hartree-Fock approximation by solving the Dyson equation.