Quantum Field Theory, Bosonization and Duality on the Half Line

TL;DR

This paper develops a bosonization method for quantum field theories on the half line, exploring boundary conditions, symmetries, and duality, and applies it to solve the massless Thirring model with various boundary conditions.

Contribution

It introduces a bosonization procedure on the half line that incorporates different boundary conditions and analyzes their effects on symmetries and duality.

Findings

Constructed operator solutions for the massless Thirring model with boundary conditions.

Analyzed the impact of boundary conditions on symmetries and duality.

Developed a framework for bosonization on the half line.

Abstract

We develop a bosonization procedure on the half line. Different boundary conditions, formulated in terms of the vector and axial fermion currents, are implemented by using in general the mixed boundary condition on the bosonic field. The interplay between symmetries and boundary conditions is investigated in this context, with a particular emphasis on duality. As an application, we explicitly construct operator solutions of the massless Thirring model on the half line, respecting different boundary conditions.