Berry phase in generalized chiral $QED_2$

TL;DR

This paper calculates the Berry phase in a generalized chiral QED2 model on a circle, revealing its connection to gauge symmetry representations and contributions to the effective action.

Contribution

It introduces a method to compute the Berry phase in a chiral gauge theory with different charges, linking it to gauge symmetry and effective action contributions.

Findings

Vacuum Berry phase is nonzero and linked to projective gauge representations.

Berry connection and curvature are explicitly calculated for vacuum and Fock states.

The vacuum Berry phase influences the effective action of the model.

Abstract

We consider the generalized chiral $QED_2$ on $S^1$ with a $U(1)$ gauge field coupled with different charges to both chiral components of a fermionic field. Using the adiabatic approximation we calculate the Berry phase and the corresponding ${\rm U}(1)$ connection and curvature for the vacuum and many particle Fock states. We show that the nonvanishing vacuum Berry phase is associated with a projective representation of the local gauge symmetry group and contributes to the effective action of the model.