  The Dirac equation, in the field of a traveling circularly polarized
electromagnetic wave and a constant magnetic field, has singular solutions,
corresponding the expansion of energy in vicinity of some singular point. These
solutions described relativistic fermions. States relating to these solutions
are not stationary. The temporal change of average energy, momentum and spin
for single and mixed states is studied in the paper. A distinctive feature of
the states is the disappearance of the longitudinal component of the average
spin. Another feature is the equivalence of the condition of fermion minimal
energy and the classical condition of the magnetic resonance. Finding such
solutions assumes the use of a transformation for rotating and co-moving frames
of references. Comparison studies of solutions obtained with the Galilean and
non-Galilean transformation shown that some parameters of the non-Galilean
transformation may be measured in high-energy physics.
