Path-Integral bosonization of a non-local interaction and its application to the study of 1-d many-body systems

TL;DR

This paper develops a path-integral bosonization method for non-local fermionic interactions, enabling analysis of 1D many-body systems like the Tomonaga-Luttinger model and its extensions, including non-Abelian cases.

Contribution

It introduces a bosonization approach for non-local interactions, generalizing existing methods and applying it to 1D many-body systems with potential for non-Abelian extensions.

Findings

Bosonized version of a non-local Thirring-like model obtained

Analysis of fermionic correlators and collective modes conducted

Method extended to non-Abelian interactions for spin systems

Abstract

We extend the path-integral approach to bosonization to the case in which the fermionic interaction is non-local. In particular we obtain a completely bosonized version of a Thirring-like model with currents coupled by general (symmetric) bilocal potentials. The model contains the Tomonaga-Luttinger model as a special case; exploiting this fact we study the basic properties of the 1-d spinless fermionic gas: fermionic correlators, the spectrum of collective modes, etc. Finally we discuss the generalization of our procedure to the non-Abelian case, thus providing a new tool to be used in the study of 1-d many-body systems with spin-flipping interactions.