Generalised chiral QED2 : Anomaly and Exotic Statistics

TL;DR

This paper investigates how the anomaly affects the quantum structure of the generalized chiral Schwinger model on a circle, revealing nonrelativistic spectra, exotic statistics, and modifications to Poincare symmetry.

Contribution

It explicitly constructs the algebra of Poincare generators in the presence of anomaly and demonstrates the role of the vacuum Berry phase in symmetry breaking.

Findings

Anomaly causes a linearly rising electric field.

Physical spectrum becomes nonrelativistic without a massive boson.

Total charge screening persists despite the background electric field.

Abstract

We study the influence of the anomaly on the physical quantum picture of the generalized chiral Schwinger model defined on the circle. We show that the anomaly i) results in the background linearly rising electric field and ii) makes the spectrum of the physical Hamiltonian nonrelativistic without a massive boson. The physical matter fields acquire exotic statistics . We construct explicitly the algebra of the Poincare generators and show that it differs from the Poincare one. We exhibit the role of the vacuum Berry phase in the failure of the Poincare algebra to close. We prove that, in spite of the background electric field, such phenomenon as the total screening of external charges characteristic for the standard Schwinger model takes place in the generalized chiral Schwinger model, too.