Chiral Magnetic Effect in QED induced by longitudinal photons

Chiral magnetic effect exists in an electron-positron strongly magnetized gas in QED. It is induced by an electric field parallel to the external field $\mathbf{\text{B}}$, like that produced by the pseudovector longitudinal mode propagating along $\mathbf{\text{B}}$. In the static limit, an electric pseudovector current is obtained in the lowest Landau level. We obtain a new axial anomaly expression in a medium of massive particles in the presence of $\mathbf{\text{B}}$, for scattering or pair creation, similar to the usual QED axial anomaly. The effect is interesting in connection to the QCD chiral magnetic case reported in current literature.