Structural Aspects of Two-Dimensional Anomalous Gauge Theories

TL;DR

This paper explores the fundamental structural properties of two-dimensional anomalous gauge theories, focusing on the Hilbert space construction, the impact of different field algebras, and the connection to the vector Schwinger model.

Contribution

It provides a detailed analysis of how the choice of field algebra affects the physical properties and the Hilbert space structure of anomalous gauge models.

Findings

Different results arise depending on whether the Hilbert space is restricted to the intrinsic local field algebra.

The vector Schwinger model limit is only consistent when defined on a specific subalgebra.

The structure of the field algebra significantly influences the physical properties of the models.

Abstract

A foundational investigation of the basic structural properties of two-dimensional anomalous gauge theories is performed. The Hilbert space is constructed as the representation of the intrinsic local field algebra generated by the fundamental set of field operators whose Wightman functions define the model. We examine the effect of the use of a redundant field algebra in deriving basic properties of the models and show that different results may arise, as regards the physical properties of the generalized chiral model, in restricting or not the Hilbert space as representation of the intrinsic local field algebra. The question referring to considering the vector Schwinger model as a limit of the generalized anomalous model is also discussed. We show that this limit can only be consistently defined for a field subalgebra of the generalized model.