Igor A. Shovkovy, Ritesh Ghosh

We review field-theoretic studies of charge transport in hot relativistic plasmas under strong magnetic fields and extend the analysis to thermal conductivity. The calculations rely on accurately determining the fermion damping rate. Using the Landau-level representation, these damping rates are computed exactly at leading order and incorporated into the Kubo formula to obtain the thermal and electrical conductivity tensors. Our analysis reveals that the underlying mechanisms of longitudinal and transverse transport differ significantly. Strong magnetic fields markedly suppress transverse transport by confining particles within localized Landau orbits, allowing transport only through quantum transitions between these discrete states. In contrast, longitudinal transport is enhanced, as it primarily depends on the reduced scattering probability of particles moving along the direction of the magnetic field. We also examine the modification of the Wiedemann--Franz law in strongly magnetized plasmas.