  Spin degrees of freedom of the Galilean covariant Dirac field in (4+1)
dimensions and its nonrelativistic counterpart in (3+1) dimensions are
examined. Two standard choices of spin operator, the Galilean covariant and
Dirac spin operators, are considered. It is shown that the Dirac spin of the
Galilean covariant Dirac field in (4+1) dimensions is not conserved, and the
role of non-Galilean boosts in its nonconservation is stressed out. After
reduction to (3+1) dimensions the Dirac field turns into a nonrelativistic
Fermi field with a conserved Dirac spin. A generalized form of the Levy-Leblond
equations for the Fermi field is given. One-particle spin states are
constructed. A particle-antiparticle system is discussed.
