  We discuss here the possibility to write the Liouville-Vlasov equation for
the Wigner-function of a spinor field coupled to a gauge field with field
strength tensor $F^{\mu\nu}$ in a curved space-time versus a local Lorentz
manifold (introduction of local Lorentz coordinates) with an appropriate
definition of a covariant derivative carried out using a spin connection
$B_{\mu}^{ab}(x)$.
