The 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. First we study the zero-temperature Casimir energy and fermion number for Dirac fields in a (2+1)-dimensional Minkowski spacetime, 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.