  We investigate electrical charge transport in hot magnetized plasma using
first-principles quantum field theoretical methods. By employing Kubo's linear
response theory, we express the electrical conductivity tensor in terms of the
fermion damping rate in the Landau-level representation. Utilizing
leading-order results for the damping rates from a recent study within a gauge
theory, we derive the transverse and longitudinal conductivities for a strongly
magnetized plasma. The analytical expressions reveal drastically different
mechanisms that explain the high anisotropy of charge transport in a magnetized
plasma. Specifically, the transverse conductivity is suppressed, while the
longitudinal conductivity is enhanced by a strong magnetic field. As in the
case of zero magnetic field, longitudinal conduction is determined by the
probability of charge carriers to remain in their quantum states without
damping. In contrast, transverse conduction critically relies on quantum
transitions between Landau levels, effectively lifting charge trapping in
localized Landau orbits. We examine the temperature and magnetic field
dependence of the transverse and longitudinal electrical conductivities over a
wide range of parameters and investigate the effects of a nonzero chemical
potential. Additionally, we extend our analysis to strongly coupled quark-gluon
plasma and study the impact of the coupling constant on the anisotropy of
electrical charge transport.
