Structural aspects of the fermion-boson mapping in two-dimensional gauge and anomalous gauge theories with massive fermions

TL;DR

This paper explores the fermion-boson mapping in two-dimensional gauge theories with massive fermions, highlighting the algebraic structures, anomalies, and the role of auxiliary and Wess-Zumino fields in the models.

Contribution

It provides a detailed analysis of the algebraic and physical implications of fermion-boson mapping in 2D gauge theories with massive fermions, including anomalous cases.

Findings

Auxiliary vector fields introduce redundant Bose algebra elements.

Chiral anomaly leads to spurious Bose field combinations in the mass operator.

Wess-Zumino fields replicate the theory without altering its algebraic or physical content.

Abstract

Using a synthesis of the functional integral and operator approaches we discuss the fermion-boson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In the $QED_2$ with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In the anomalous chiral $QED_2$ with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of $\theta$-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content.