  When the Zeeman energy approaches the characteristic kinetic energy of
electrons, Landau quantization becomes important. In the vicinity of magnetars,
the Zeeman energy can even be relativistic. We start from the Dirac equation
and derive a kinetic equation for electrons, focusing on the phenomenon of
Landau quantization in such ultra-strong but constant magnetic fields,
neglecting short-scale quantum phenomena. It turns out that the usual
relativistic gamma factor of the Vlasov equation is replaced by an energy
operator, depending on the spin state, and also containing momentum
derivatives. Furthermore, we show that the energy eigenstates in a magnetic
field can be computed as eigenfunctions of this operator. The dispersion
relation for electrostatic waves in a plasma is computed, and the significance
of our results is discussed.
