Axial anomaly of QED in a strong magnetic field and noncommutative anomaly
نویسنده
چکیده
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 UA(1) anomaly of QED in a strong magnetic field is closely related to the nonplanar axial anomaly of a conventional noncommutative U(1) gauge theory.
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