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.

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

References in corpus (1)

• Dynamics of O(N) Model in a Strong Magnetic Background Field as a Modified Noncommutative Field Theory

Cited by in corpus (3)

• Spontaneous electromagnetic superconductivity of vacuum in strong magnetic field: evidence from the Nambu--Jona-Lasinio model
• Chiral asymmetry and axial anomaly in magnetized relativistic matter
• Adler-Bell-Jackiw anomaly in VSR electrodynamics