  The concept of the Wigner function is used to construct a semi-classical
kinetic theory describing the evolution of the axial-current phase-space
density of spin-1/2 particles in the relaxation time approximation. The
resulting approach can be used to study spin-polarization effects in
relativistic matter, in particular, in heavy-ion collisions. An expression for
the axial current based on the classical treatment of spin is also introduced
and we show that it is consistent with earlier calculations using Wigner
functions. Finally, we derive non-equilibrium corrections to the spin tensor,
which are used to define, for the first time, the structure of spin transport
coefficients in relativistic matter.
