Chiral current generation in QED by longitudinal photons

TL;DR

This paper demonstrates the generation of a chiral electric current in a strongly magnetized electron-positron gas within QED, driven by longitudinal photons and related to an anomaly in the axial current, with implications for chiral magnetic effects.

Contribution

It introduces a novel mechanism for chiral current generation in QED involving longitudinal photon modes and massive fermions, extending previous massless and chemical potential assumptions.

Findings

A pseudovector electric current propagates along the magnetic field in a magnetized QED medium.

The chiral current is linked to an anomaly relation similar to the Adler-Bell-Jackiw anomaly.

Electrons and positrons contribute to the current via scattering and pair creation with longitudinal photons.

Abstract

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 B as a chiral magnetic effect in QED. It is triggered by a perturbative electric field parallel to B, associated to a pseudovector longitudinal mode propagating along B. An electromagnetic chemical potential was introduced, but our results remain valid even for vanishing chemical potential. 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 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