Hard thermal loops in a magnetic field and the chiral anomaly Original Research Article

The fermionic dispersion relation in the presence of a background magnetic field and a high temperature QED plasma is calculated exactly in the external field, using the Hard Thermal Loop effective action. As the field strength increases there is a smooth transition from the weak-field (qB ⪡ q2T2) thermal dispersion relations to the vacuum Landau levels when the backgroun field is much stronger than any thermal effects (qB ⪢ q2T2). The self-energy at finite field strength acquires an imaginary part. The spectral width becomes important for critical field strengths (qB ≈ q2T2), necessitating the use of the full spectral function. It is shown that the spectral function satisfies the usual condition of normalization and causality. Using the exact spectral function I also show that the production of chirality in an external electromagnetic field at high temperature is unaffected by the presence of the thermal masses of the fermions.