  We study the stability of the ordinary Landau Fermi liquid phase for
interacting, spinless electrons. We require causality and demand that the Pauli
principle be obeyed. We find a phase diagram determined by two parameters: the
particle density and the interaction strength. We find that the homogeneous,
constant density Fermi liquid phase of a spinless Fermion gas is {\em never}
stable in 1D, but that it may have a restricted domain of stability in 2D.
