Relativistic Landau problem at finite temperature

We study the zero temperature Casimir energy and fermion number for Dirac fields in a 2+1-dimensional Minkowski space-time, in the presence of a uniform magnetic field perpendicular to the spatial manifold. Then, we go to the finite-temperature problem with a chemical potential, introduced as a uniform zero component of the gauge potential. By performing a Lorentz boost, we obtain Hall's conductivity in the case of crossed electric and magnetic fields.