Constraint and confinement in strongly correlated fermion systems

We discuss in this paper the low energy properties of a liquid of fermions coupling to a U(1) gauge field at wavevectors q < Lambda much less than k(F ) at dimensions larger than one, where Lambda much less than k(F) is a high momentum cutoff and k(F) is the Fermi wave vector. In particular, we shall consider the e(2) --> infinity limit where charge and current fluctuations at wave vectors q < Lambda are forbidden, and the problem reduces to the p roblem of imposing constraint that no charge and current fluctuations are a llowed in the liquid of fermions. Within a bosonization approximation, we s how that the low energy properties of the system can be described as a Ferm i liquid of chargeless quasiparticles which has vanishing wavefunction over lap with the bare fermion's in the system. The case of a two component syst em (t-J model) will also be discussed.