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Relativistic analogue of the Pauli equation and Dirac electron states in strong magnetic fields

In a constant magnetic field, an exact unitary transformation is found, which reduces the Dirac equation to a two-component relativistic Pauli equation analogue. New conserved quantities are discovered. An interplay between the spin and orbital motions of a Dirac particle is revealed, which is especially dramatic in homogeneous above-Schwinger fields, where the Pauli equation analogue, in itself, allows velocities exceeding the speed of light. An exact equation for the electron spin in a strong magnetic field is obtained, which turns into the Bargmann-Michel-Telegdi equation in the high-energy limit.