Anomaly and Exotic Statistics in One Dimension

TL;DR

This paper investigates how anomalies affect the quantum properties of the chiral Schwinger model in one dimension, revealing exotic statistics and altered Poincare algebra, differing from the standard Schwinger model.

Contribution

It demonstrates the impact of anomalies on the physical quantum picture of the chiral Schwinger model, including the emergence of exotic statistics and modifications to the Poincare algebra.

Findings

Absence of charge screening and mass generation in the CSM on S^1.

Presence of a linearly rising electric field due to anomaly.

Altered Poincare algebra in the CSM caused by anomaly.

Abstract

We study the influence of the anomaly on the physical quantum picture of the chiral Schwinger model (CSM) defined on $S^1$. We show that such phenomena as the total screening of charges and the dynamical mass generation characteristic for the standard Schwinger model do not take place here. Instead of them, the anomaly results in the background linearly rising electric field or, equivalently, in the exotic statistics of the physical matter field. We construct the algebra of the Poincare generators and show that it differs from the Poincare one. For the CSM on $R^1$, the anomaly influences only the mass generation mechanism.