Effective Lagrangian of Thermal QED with External Magnetic Field and the Static Limit of the Polarization Operator

A low-temperature expansion of QED one-loop effective Lagrangian valid for a wide range of parameters is presented in a form of finite sums of elementary functions. Starting from the effective action components of the one-loop polarization operator responsible for Hall conductivity and Debye screening are obtained. It is shown that in a strong background magnetic field the Debye radius depends on spatial direction.