  We review the calculation of polarization in a relativistic fluid within the
framework of statistical quantum field theory. We derive the expressions of the
spin density matrix and the mean spin vector both for a single quantum
relativistic particle and for a quantum free field. After introducing the
formalism of the covariant Wigner function for the scalar and the Dirac field,
the relation between spin density matrix and the covariant Wigner function is
obtained. The formula is applied to the fluid produced in relativistic nuclear
collisions by using the local thermodynamic equilibrium density operator and
recovering previously known formulae. The dependence of these results on the
spin tensor and pseudo-gauge transformations of the stress-energy tensor is
addressed.
