  We present a relativistic formulation of the quantum Hall effect on Haldane
sphere. An explicit form of the pseudopotential is derived for the relativistic
quantum Hall effect with/without mass term. We clarify particular features of
the relativistic quantum Hall states with the use of the exact diagonalization
study of the pseudopotential Hamiltonian. Physical effects of the mass term to
the relativistic quantum Hall states are investigated in detail. The mass term
acts as an interpolating parameter between the relativistic and
non-relativistic quantum Hall effects. It is pointed out that the mass term
unevenly affects the many-body physics of the positive and negative Landau
levels as a manifestation of the "parity anomaly". In particular, we explicitly
demonstrate the instability of the Laughlin state of the positive first
relativistic Landau level with the reduction of the charge gap.
