Electrical conductivity of hot relativistic plasma in a strong magnetic field

We employ first-principles quantum field theoretical methods to investigate the longitudinal and transverse electrical conductivities of a strongly magnetized hot QED plasma at the leading order in coupling. The analysis utilized the fermion damping rate in the Landau-level representation obtained recently. In the relativistic regime, both conductivities exhibit a scaling behavior given by σ∥,⊥ = T σ̃∥,⊥, where σ̃∥,⊥ are functions of the dimensionless ratio |eB|/T² (here T denotes the temperature and B the magnetic field). As |eB|/T² increases, both conductivities initially decrease, reach minima, and then exhibit growths when the lowest Landau level dominates. However, the mechanisms for the transverse and longitudinal conductivities differ significantly, leading to a strong suppression of the former in comparison to the latter. Additionally, we extend our analysis to a magnetized quark-gluon plasma, although the approximation's validity breaks down in QCD at strong coupling.