Electric Susceptibility for Strongly Magnetized Electron-positron Plasma at Finite Temperature and Density

We study the electric response of a relativistic electron-positron plasma at finite density and temperature in the presence of a strong magnetic field. The results are found by calculating the polarization tensor of such a system in the one-loop approximation. It was determined that a photon traveling through this medium acquires a Debye mass that depends on the magnitude of the magnetic field, temperature and chemical potential. We also found that the system electric susceptibility is anisotropic, with a component transverse to the magnetic field, which is that of vacuum, and a longitudinal component, which decreases with the temperature and density. Our findings can be of interest in the study of solid-state planar systems such as graphene. They can also be used to study the behavior of quarks in relativistic heavy ion collisions at intermediate energies, where the quark matter can be in a high density and moderate temperature state, as well as in the astrophysics of compact objects such as neutron stars