  In this paper we describe the transformation properties of quantum
entanglement encoded in a pair of spin 1/2 particles described via Dirac
bispinors. Due to the intrinsic parity-spin internal structure of the
bispinors, the joint state is a four-qubit state exhibiting multipartite
entanglement, and to compute global correlation properties we consider the
averaged negativities over each possible bi-partition. We also consider
specific bipartitions, such as the spin-spin and the particle-particle
bipartitions. The particle-particle entanglement, between all degrees of
freedom of one particle and all degrees of freedom of the other particle, is
invariant under boosts if each particle has a definite momentum, although the
spin-spin entanglement is degraded for high speed boosts. Correspondingly, the
mean negativities are not invariant since the boost drives changes into
correlations encoded in specific bipartitions. Finally, the results presented
in the literature about spin-momentum entanglement are recovered by considering
the projection of bispinorial states into positive intrinsic parity, and some
striking differences between the appropriate approach for this case and the one
usually treated in the literature are discussed.
