  We study a system of fermions interacting with a gauge field which can be
used to describe either spin liquid or $\nu=1/2$ Quantum Hall state. We propose
a generalized model with a dimensionless parameter $N$. We evaluate the
properties of the model in both limits $N \gg 1$ and $N \ll 1$ and deduce the
properties of the model in the most physically intersting case of $N=1,2$. At
$N \ll 1$ the motion of the fermions becomes one dimensional. This allows us to
obtain the fermion Green function and response functions applying bozonization
method in this limit.
