Dynamics of fermions coupling to a U(1) gauge field in the limit $e^2\to\infty$

We study in this paper the properties of a gas of fermions coupling to a U(1) gauge field at wavevectors $q<\Lambda<<k_F$ at dimensions larger than one, where $\Lambda<<k_F$ is a high momentum cutoff and $k_F$ is the fermi wave vector. In particular, we shall consider the $e^2\to\infty$ limit where charge and current fluctuations at wave vectors $q<\Lambda$ are forbidden. Within a bosonization approximation, effective actions describing the low energy physics of the system are constructed, where we show that the system can be described as a fermion liquid formed by chargeless quasi-particles which has vanishing wavefunction overlap with the bare fermions in the system.