Effective lowering of dimensionality in the strongly correlated two dimensional electron gas

We study a system of fermions interacting with a gauge field which can be used to describe either a spin liquid or the {ν}=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{}1 and N{}1 and deduce the properties of the model in the most physically interesting case of N=1,2. At N{}1 the motion of the fermions becomes one dimensional. By applying the bosonization method in this limit, we obtain the fermion Green function and response functions.