Bosonization theory of fermions interacting via a Coulomb potential in the limit e2→∞

We study in this paper the properties of a gas of fermions interacting via a scalar potential v(q)=4πe2/q2 for q<Λ<<kF at dimensions larger than 1, where Λ<<kF is a high-momentum cutoff and kF is the Fermi wave vector. In particular, we shall consider the e2→∞ limit, where charge fluctuations at wave vectors q<Λ 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 Fermi liquid formed by chargeless quasiparticles, which has vanishing wave function overlap with the bare fermions in the system