Nonlinear Bosonization and Refermionization in One Dimension with the Keldysh Functional Integral

TL;DR

This paper presents a comprehensive method for bosonization and refermionization in one-dimensional systems using the Keldysh functional integral, including interaction effects and applications to bosonic and fermionic particles.

Contribution

It introduces a self-contained approach to bosonization and refermionization with explicit calculations of interaction terms and mappings between bosonic and fermionic excitations.

Findings

Derived the leading interaction term in the Tomonaga-Luttinger liquid

Validated the approach by comparing with Matsubara framework calculations

Mapped phonons to non-interacting fermionic quasiparticles

Abstract

We develop a self-contained approach to bosonization and refermionization using the Keldysh functional integral. Starting from fermionic particles, we bosonize the system and obtain a description in terms of the Tomonaga-Luttinger liquid, with, in addition, an infinite series of interaction terms arising from the curvature of the fermionic particle spectrum. We explicitly calculate the leading interaction term and check its consistency with a different approach based on the Matsubara framework, within which we calculate the second leading interaction term, as well. Moreover, we bosonize weakly and strongly interacting bosonic particles, and, finally, refermionize interacting phonons into non-interacting fermionic quasiparticles. The work culminates in a map between bosonic and fermionic particles and effective bosonic and fermionic excitations, representing phonons and fermionic quasiparticles.