The Luttinger-Schwinger Model

TL;DR

This paper solves the (1+1)D Luttinger-Schwinger model of massless Dirac fermions with non-local interactions, using boson-fermion correspondence, and explores gauge invariance, anomalies, and the connection to the Thirring-Schwinger model.

Contribution

It provides a complete solution to the Luttinger-Schwinger model and develops a formalism for gauge-invariant Green functions, including the effects of anomalies and large gauge transformations.

Findings

Complete solution of the Luttinger-Schwinger model

Formalism for gauge-invariant Green functions

Connection to the Thirring-Schwinger model via regularization

Abstract

We study the Luttinger-Schwinger model, i.e. the (1+1) dimensional model of massless Dirac fermions with a non-local 4-point interaction coupled to a U(1)-gauge field. The complete solution of the model is found using the boson-fermion correspondence, and the formalism for calculating all gauge invariant Green functions is provided. We discuss the role of anomalies and show how the existence of large gauge transformations implies a fermion condensate in all physical states. The meaning of regularization and renormalization in our well-defined Hilbert space setting is discussed. We illustrate the latter by performing the limit to the Thirring-Schwinger model where the interaction becomes local.