  The behavior of relativistic particles in an electric and/or magnetic field
is considered in the general case when the direction of propagation may differ
from the direction of the field. A special attention is paid to the spin
splitting and the ensuing Larmor precession frequency of both neutral and
charged particles. For both neutral and charged particles, the Larmor frequency
shows a longitudinal motional red shift. For a neutral particle, there is a
dynamical upper bound, which depends on both the mass and the transverse
momentum of the particle; moreover, the transverse motion leads to a blue shift
of the Larmor frequency. For a charged particle, the longitudinal motional
decrease of the spin splitting is determined by the formation of Landau levels
and it has no upper limit. Unlike the nonrelativistic limit, the relativistic
spin splitting depends on the Landau levels and decreases for higher Landau
levels, thereby signalling the presence of a Landau ladder red shift effect.
