Berry phase connection and anomaly in two dimensions

TL;DR

This paper investigates the Berry phase connection in a two-dimensional chiral Schwinger model, revealing how zero curvature components influence physical phenomena like electric fields despite not contributing to the curvature.

Contribution

It provides a direct calculation of the vacuum Berry phase connection and uncovers its physical implications in a two-dimensional gauge theory.

Findings

Zero curvature part affects the total Berry connection.

The connection contributes to linearly rising electric fields.

The zero curvature component does not influence the curvature itself.

Abstract

For the generalized chiral Schwinger model defined on the circle, a direct calculation of the zero curvature part of the vacuum Berry phase connection is given. Although this part does not contribute to the curvature, it is shown to attach several features to the total connection and to produce a physical background of linearly rising electric fields.