Curvature-spin coupling from the semi-classical limit of the Dirac   equation
  The notion of a classical particle is inferred from Dirac quantum fields on a curved space-time, by an eikonal approximation and a localization hypothesis for amplitudes. This procedure allows to define a semi-classical version of the spin-tensor from internal quantum degrees of freedom, which has a Papapetrou-like coupling with the curvature. 
F. Cianfrani, G. Montani