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 quantum electrodynamics (QED) plasma at the leading order in coupling. The analysis employs the fermion damping rate in the Landau-level representation, calculated with full kinematics and exact amplitudes of one-to-two and two-to-one QED processes. In the relativistic regime, both conductivities exhibit an approximate scaling behavior described by $\sigma_{\parallel,\perp} = T \tilde{\sigma}_{\parallel,\perp}$, where $\tilde{\sigma}_{\parallel,\perp}$ are functions of the dimensionless ratio $|eB|/T^2$ (with $T$ denoting temperature and $B$ magnetic field strength). We argue that the mechanisms for the transverse and longitudinal conductivities differ significantly, leading to a strong suppression of the former in comparison to the latter.