Dirac equations in curved space-time versus Papapetrou spinning   particles
  We find out classical particles, starting from Dirac quantum fields on a curved space-time, by an eikonal approximation and a localization hypothesis for amplitudes. We recover the results by Mathisson-Papapetrou, hence establishing a fundamental correspondence between the coupling of classical and quantum spinning particles with the gravitational field. 
Francesco Cianfrani, Giovanni Montani