  We start the paper with a brief presentation of the main characteristics of
graphene, and of the Dirac theory of massless fermions in 2+1 dimensions
obtained as the associated low-momentum effective theory, in the absence of
external fields. We then summarize the main steps needed to obtain the Hall
conductivity in the effective theory at finite temperature and density, with
emphasis on its dependence on the phase of the Dirac determinant selected
during the evaluation of the effective action. Finally, we discuss the
behavior, under gauge transformations, of the contribution due to the lowest
Landau level, and interpret gauge transformations as rotations of the
corresponding spinors around the magnetic field.
