Expressing Products of Fermi Fields in terms of Fermi Sea Displacements

TL;DR

This paper extends bosonization techniques for Fermi surfaces by introducing Bose fields linked to Fermi sea displacements, enabling analysis of high-energy single particle excitations and reproducing key commutation and correlation functions.

Contribution

It introduces a novel bosonization approach based on Fermi sea displacements, allowing study of short wavelength fluctuations and high-energy excitations.

Findings

Most commutation rules are exactly reproduced.

Dynamical correlation functions match the free theory.

Provides an explicit realization of the current algebra representation.

Abstract

An attempt is made to generalise the ideas introduced by Haldane and others regarding Bosonizing the Fermi surface. The present attempt involves introduction of Bose fields that correspond to displacements of the Fermi sea rather than just the Fermi surface. This enables the study of short wavelength fluctuations of the Fermi surface and hence the dispersion of single particle excitations with high energy. The number conserving product of two Fermi fields is represented as a simple combination of these Bose fields. It is shown that most(!) commutation rules involving these number conserving products are reproduced exactly, as are the dynamical correlation functions of the free theory. Also the work of Sharp, Menikoff and Goldin has shown that the field operator may be viewed as a unitary representation of the current algebra. An explicit realisation of this unitary representation is given in terms of canonical conjugate of the density operator.