Non-adiabatic and finite-temperature corrections to pseudoscalar terms

Investigate the non-adiabatic regimes of massive fermions in a constant magnetic field and spatially modulated electric fields, where real-particle production can occur, together with finite-temperature and radiative corrections to the pseudoscalar terms in the axial Ward identity.

Background

The paper derives the axial Ward identity for massive fermions subjected to a constant magnetic field and a spatially modulated perturbative electric field, focusing on the adiabatic regime in which the electric-field frequency is below the threshold for real-particle production. In this regime, a local axial-charge source survives because the anomaly contribution from higher Landau levels is not canceled by the pseudoscalar term.

The authors explicitly identify the non-adiabatic regime, where real-particle production becomes possible, as well as finite-temperature and radiative modifications of the pseudoscalar contribution, as topics requiring further investigation. These extensions would test the robustness of higher-Landau-level dominance and the local axial-charge source beyond the approximations used in the Letter.