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

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.

arXiv comment18 pp, no figure. v2: The version accepted to be publidhed in PRD

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• The Chiral Magnetic Effect and Axial Anomalies
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• Photon Magnetic Moment and Vacuum Magnetization in an Asymptotically Large Magnetic Field
• Towards Noncommutative Fuzzy QED
• A note on broken dilatation symmetry in planar noncommutative theory
• Adler-Bell-Jackiw anomaly in VSR electrodynamics
• Path integral analysis of the axial anomaly in Very Special Relativity
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