Algebraic Isomorphism In Two-Dimensional Anomalous Gauge Theories

TL;DR

This paper analyzes the operator solution of the anomalous chiral Schwinger model, establishing an algebraic isomorphism between gauge invariant and noninvariant descriptions, and clarifies the role of the Theta-vacuum and model equivalences.

Contribution

It provides a rigorous algebraic framework for understanding the structure of anomalous gauge theories and clarifies the limitations of certain model equivalences.

Findings

Established isomorphism between gauge invariant and noninvariant field algebras.

Showed that Theta-vacuum representation cannot be derived from the intrinsic field algebra.

Demonstrated the non-equivalence of vector and chiral Schwinger models in the algebraic framework.

Abstract

The operator solution of the anomalous chiral Schwinger model is discussed on the basis of the general principles of Wightman field theory. Some basic structural properties of the model are analyzed taking a careful control on the Hilbert space associated with the Wightman functions. The isomorphism between gauge noninvariant and gauge invariant descriptions of the anomalous theory is established in terms of the corresponding field algebras. We show that (i) the Theta-vacuum representation and (ii) the suggested equivalence of vector Schwinger model and chiral Schwinger model cannot be established in terms of the intrinsic field algebra.