  We give a direct link between description of Dirac particles in the abstract
framework of unitary representation of the Poincar\'e group and description
with the help of the Dirac equation. In this context we discuss in detail the
spin operator for a relativistic Dirac particle. We show also that the spin
operator used in quantum field theory for spin $s=1/2$ corresponds to the
Foldy-Woutheysen mean-spin operator.
