Improvement of the Calculation of Scattering Amplitudes with External   Fermions
  In this paper, we present an improvement of a method for computing scattering amplitudes that include external (polarized) fermions with the following features: the formulas are quite general and work for different kinematic configurations and different external masses, they are explicitly covariant, they do not depend on a specific representation of the Dirac matrices and they have a meaningful limit when the masses tend to 0. The results presented make use of some well known formulas describing the density matrices in terms of projection operators within a more general formalism. Since our formulas intend to be as general as possible, we also take into account the possibility of a transverse polarization for massless fermions. 
E. Chopin (LAPTH)