A derivation of the Boltzmann-Vlasov equation from multiple scattering   using the Wigner function
  A derivation is given of the Boltzmann-Vlasov equation beginning from multiple scattering considerations. The motivation for the discussion, which is purely pedagogical in nature, is the current interest in understanding the origins of transport equations in terms of rigorous field-theory descriptions, or, as in this case, exact nonrelativistic formulations. 
J. M. Eisenberg