Unification of the Soluble Two-dimensional vector coupling models

TL;DR

This paper develops a comprehensive two-dimensional fermion-vector meson coupling theory, unifying various soluble models like the Schwinger model, by solving for Green's functions with multiple parameters.

Contribution

It introduces a four-parameter framework that unifies existing soluble models in two-dimensional fermion-vector coupling theories.

Findings

Complete set of Green's functions derived.

Model reduces to known soluble models in specific limits.

Includes both vector and axial vector couplings.

Abstract

The general theory of a massless fermion coupled to a massive vector meson in two dimensions is formulated and solved to obtain the complete set of Green's functions. Both vector and axial vector couplings are included. In addition to the boson mass and the two coupling constants, a coefficient which denotes a particular current definition is required for a unique specification of the model. The resulting four parameter theory and its solution are shown to reduce in appropriate limits to all the known soluble models, including in particular the Schwinger model and its axial vector variant.