  We find all spin operators for a Dirac particle satisfying the following very
general conditions: (i) spin does not convert positive (negative) energy states
into negative (positive) energy states, (ii) spin is a pseudo-vector, and (iii)
eigenvalues of the projection of a spin operator on an arbitrary direction are
independent of this direction (isotropy condition). We show that there are four
such operators and all of them fulfill the standard su(2) Lie algebra
commutation relations. Nevertheless, only one of them has a proper
non-relativistic limit and acts in the same way on negative and positive energy
states. We show also that this operator is equivalent to the Newton-Wigner spin
operator and Foldy-Wouthuysen mean-spin operator. We also discuss another
operators proposed in the literature.
