Bosonization theory of fermions interacting via a confining potential

Abstract

We study in this paper the properties of a gas of fermions interacting {\em via} a scalar potential $v(q)=4\pi e^2/q^2$ for $q<\Lambda <<k_F$ at dimensions larger than one, where $\Lambda$ 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 the potential becomes confining. Within a bosonization approximation, effective Hamiltonians describing the low energy physics of the system are constructed, where we show that the system can be described as a fermi liquid formed by chargeless quasi-particles which has vanishing wavefunction overlap with the bare fermions in the system.

15 pages