  We study 1-loop effects for massless Dirac fields in two spatial dimensions,
coupled to homogeneous electromagnetic backgrounds, both at zero and at finite
temperature and density. In the case of a purely magnetic field, we analyze the
relationship between the invariance of the theory under large gauge
transformations, the appearance of Chern-Simons terms and of different Berry's
phases. In the case of a purely electric background field, we show that the
effective Lagrangian is independent of the chemical potential and of the
temperature. More interesting: we show that the minimal conductivity, as
predicted by the quantum field theory, is the right multiple of the
conductivity quantum and is, thus, consistent with the value measured for
graphene, with no extra factor of pi in the denominator.
