Anomaly of conserved and nonconserved axial charges in Hamiltonian lattice gauge theory

TL;DR

This paper examines the axial anomaly in Hamiltonian lattice gauge theory, highlighting differences between conserved and nonconserved axial charges and demonstrating that the conserved charge accurately reproduces the anomaly in the continuum limit.

Contribution

It clarifies the distinction between conserved and nonconserved axial charges in Hamiltonian lattice gauge theory and shows the conserved charge's correctness in reproducing the axial anomaly.

Findings

Conserved axial charge reproduces the axial anomaly in the continuum limit.

Nonconserved axial charge differs from the conserved one by higher-order lattice spacing terms.

The study provides insights into doubler artifacts in Hamiltonian lattice gauge theory.

Abstract

We investigate the axial anomaly in Hamiltonian lattice gauge theory. The definition of axial charge operators is ambiguous, especially between conserved and nonconserved axial charges. While these charges appear to differ only by a higher-order term in lattice spacing, they do not coincide in the continuum limit. We demonstrate, through analytical and numerical calculations in 1+1 dimensions, that the conserved axial charge correctly reproduces the axial anomaly relation in continuous spacetime. Our finding would serve as a valuable lesson about doubler artifact in Hamiltonian time evolution of lattice gauge theory.