Finite Density QED at Strong Magnetic Field

In this Thesis we study the effect of a dense medium on the quantum properties of a relativistic electron-positron plasma under a magnetic field. From the calculation of the photon polarization operator depending on temperature, chemical potential, and the magnetic field; we study how the electric susceptibility of the strongly magnetized plasma is charged with temperature and density. In the same manner we study the dependence of the Debye mass with density. Then we investigated the phenomenon of magnetic catalysis of chiral symmetry breaking for a dense medium. We found that there exist a critical value of the chemical potential where a first-order phase transition takes place for the system to regain its chiral symmetry. Our results can be on interest for the astrophysics of compact objects and for planar condensed materials with Dirac Hamiltonians as graphene