  We derive a relativistic-covariant spin operator for massive case directly
from space-time symmetry in Minkowski space-time and investigate the physical
properties of a derived spin operator. In the derivation we require only two
conditions: First, a spin operator should be the generator of the SU(2) little
group of the Poincare group. Second, a spin operator should covariantly
transform under the Lorentz transformation. A space inversion transformation is
shown to play a role to derive a unique relativistic-covariant spin operator,
we call the field spin operator, whose eigenvalue labels the spin of a massive
(classical) field that provides the irreducible representation space of the
Poincare group. The field spin becomes the covariant spin in the covariant
Dirac representation, which is shown to be the only spin that describes the
Wigner rotation properly in the covariant Dirac representation. Surprisingly,
the field spin also gives the non-covariant spin, which is the FW spin for the
positive energy state. We also show that the field spin operator is the unique
spin operator that generate the (internal) SU(2) little group transformation of
the Poincare group properly.
