Bosonization theory of fermions interacting via a confining potential

TL;DR

This paper develops a bosonization approach to analyze a fermion gas with a confining scalar potential, revealing a Fermi liquid of chargeless quasi-particles with no overlap with original fermions.

Contribution

It introduces a bosonization framework for fermions with a confining potential and characterizes the resulting low-energy quasiparticles.

Findings

System behaves as a Fermi liquid of chargeless quasiparticles

Quasiparticles have vanishing wavefunction overlap with bare fermions

Effective Hamiltonians describe low-energy physics

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.