Axial anomaly of QED in a strong magnetic field and noncommutative anomaly

TL;DR

This paper calculates the axial anomaly in QED under a strong magnetic field, revealing a dimensional reduction to 2D and linking it to noncommutative QED anomalies, thus advancing understanding of quantum anomalies in extreme conditions.

Contribution

It demonstrates the dimensional reduction of QED in a strong magnetic field and connects the axial anomaly to noncommutative QED anomalies, providing new insights into quantum field behavior under extreme magnetic conditions.

Findings

Dimensional reduction from 4D to 2D in the lowest Landau level regime.

The axial anomaly in strong magnetic fields resembles that of a 2D massless Schwinger model.

The QED axial anomaly is related to noncommutative QED anomalies.

Abstract

The Adler-Bell-Jackiw (ABJ) anomaly of a 3+1 dimensional QED is calculated in the presence of a strong magnetic field. It is shown that in the regime with the lowest Landau level (LLL) dominance a dimensional reduction from D=4 to D=2 dimensions occurs in the longitudinal sector of the low energy effective field theory. In the chiral limit, the resulting anomaly is therefore comparable with the axial anomaly of a two dimensional massless Schwinger model. It is further shown that the U(1) axial anomaly of QED in a strong magnetic field is closely related to the ``nonplanar'' axial anomaly of a conventional noncommutative QED.