  We present a fermion model that is, as we suggest, a natural 2D analogue of
the Luttinger model. We derive this model as a partial continuum limit of a 2D
spinless lattice fermion system with local interactions and away from half
filling. In this derivation, we use certain approximations that we motivate by
physical arguments. We also present mathematical results that allow an exact
treatment of parts of the degrees of freedom of this model by bosonization, and
we propose to treat the remaining degrees of freedom by mean field theory.
