Finite-temperature relativistic Landau problem and the relativistic quantum Hall effect

This paper presents a study of the free energy and particle density of the relativistic Landau problem, and their relevance to the quantum Hall effect. We study first 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.