EFFECTIVE LOWERING OF DIMENSIONALITY IN THE STRONGLY CORRELATED 2-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 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 >> 1 and N << 1 and deduce the properties of the model in the most physically in teresting case of N = 1, 2. At N << 1 the motion of the fermions becom es one dimensional. By applying the bosonization method in this limit, we obtain the fermion Green function and response functions.