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Chiral current generation in QED by longitudinal photons. (English) Zbl 1342.81707
Summary: We report the generation of a pseudovector electric current having imbalanced chirality in an electron-positron strongly magnetized gas in QED. It propagates along the external applied magnetic field $${\mathbf B}$$ as a chiral magnetic effect in QED. It is triggered by a perturbative electric field parallel to $${\mathbf B}$$, associated to a pseudovector longitudinal mode propagating along $${\mathbf B}$$. An electromagnetic chemical potential was introduced, but our results remain valid even when it vanishes. A nonzero fermion mass was assumed, which is usually considered vanishing in the literature. In the quantum field theory formalism at finite temperature and density, an anomaly relation for the axial current was found for a medium of massive fermions. It bears some analogy to the Adler-Bell-Jackiw anomaly. From the expression for the chiral current in terms of the photon self-energy tensor in a medium, it is obtained that electrons and positrons scattered by longitudinal photons (inside the light cone) contribute to the chiral current, as well as the to pair creation due to longitudinal photons (out of light cone). In the static limit, an electric pseudovector current is obtained in the lowest Landau level.
##### MSC:
 81V10 Electromagnetic interaction; quantum electrodynamics 81T28 Thermal quantum field theory 81T50 Anomalies in quantum field theory 82D10 Statistical mechanical studies of plasmas 82B30 Statistical thermodynamics 81V70 Many-body theory; quantum Hall effect
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