  We solve a model that describes an interacting electron gas in the
half-filled lowest Landau level on a thin torus, with radius of the order of
the magnetic length. The low energy sector consists of non-interacting,
one-dimensional, neutral fermions. The ground state, which is homogeneous, is
the Fermi sea obtained by filling the negative energy states and the excited
states are gapless neutral excitations out of this one-dimensional sea.
Although the limit considered is extreme, the solution has a striking
resemblance to the composite fermion description of the bulk $\nu=1/2$
state--the ground state is homogeneous and the excitations are neutral and
gapless. This suggests a one-dimensional Luttinger liquid description, with
possible observable effects in transport experiments, of the bulk state where
it develops continuously from the state on a thin torus as the radius
increases.
