  We study Faraday rotation in the quantum relativistic limit. Starting from
the photon self-energy in the presence of a constant magnetic field the
rotation of the polarization vector of a plane electromagnetic wave which
travel along the fermion-antifermion gas is studied. The connection between
Faraday Effect and Quantum Hall Effect (QHE) is discussed. The Faraday Effect
is also investigated for a massless relativistic (2D+1)-dimensional fermion
system which is derived by using the compactification along the dimension
parallel to the magnetic field. The Faraday angle shows a quantized behavior as
Hall conductivity in two and three dimensions.
