EXACT DIAGONALIZATION OF THE FULL PROPAGATOR IN IQHE AND FQHE CONFIGURATIONS

It is argued that the free-electron wave functions In crossed magnetic and electric fields exactly diagonalize the full propagator for the Coulomb interacting electron gas. The result follows under the assumption that the translational invariance is unbroken in the ground state. We derive this property for the 2D electron gas, usually discussed in QHE context. This properly is also valid for the general 3D electron systems retaining translational invariance in the plane orthogonal to the magnetic field. A simple diagonalized formula for the propagator is also presented.