Loop Variables for compact two-dimensional quantum electrodynamics

TL;DR

This paper introduces a gauge-invariant variable framework for compact 2D quantum electrodynamics with massless fermions, enabling precise analysis of the spectrum, anomalies, and gauge invariance without large gauge dependence.

Contribution

It develops a novel gauge-invariant variable approach for compact 2D QED, facilitating regularization and analysis of spectral and anomaly properties.

Findings

Zero mode spectrum is not equally spaced, unlike non-compact case.

The theory's spectrum does not resemble a free scalar boson.

All states, including the vacuum, are invariant under large gauge transformations.

Abstract

Variables parametrized by closed and open curves are defined to reformulate compact U(1) Quantum Electrodynamics in the circle with a massless fermion field. It is found that the gauge invariant nature of these variables accommodates into a regularization scheme for the Hamiltonian and current operators that is specially well suited for the study of the compact case. The zero mode energy spectrum, the value of the axial anomaly and the anomalous commutators this model presents are hence determined in a manifestly gauge invariant manner. Contrary to the non compact case, the zero mode spectrum is not equally spaced and consequently the theory does not lead to the spectrum of a free scalar boson. All the states are invariant under large gauge transformations. In particular, that is the case for the vacuum, and consequently the $\theta$-dependence does not appear.