Construction by bosonization of a fermion-phonon model

TL;DR

This paper extends the massless Thirring model to include local fermion-phonon interactions, providing an exact bosonization solution with rigorous mathematical foundations and proofs.

Contribution

It introduces a mathematically rigorous construction and solution of a fermion-phonon model as a limit of a Luttinger-phonon model, advancing bosonization techniques.

Findings

Exact solution of the fermion-phonon model via bosonization

Mathematically rigorous treatment with complete proofs

Framework as a limit of a Luttinger-phonon model

Abstract

We discuss an extension of the (massless) Thirring model describing interacting fermions in one dimension which are coupled to phonons and where all interactions are local. This fermion-phonon model can be solved exactly by bosonization. We present a construction and solution of this model which is mathematically rigorous by treating it as a limit of a Luttinger-phonon model. A self-contained account of the mathematical results underlying bosonization is included, together with complete proofs.