state of the entangled pair undergoes an $SU(2)$ Wigner rotation. Since $[SU(2)\times{SU(2)}]/Z_2$ is isomorphic to $SO(4)$, which contains 3-dimensional rotations $SO(3)$ as a sub-group; in group theoretical terms the entangled system transforms as ${\bf 2}\otimes{\bf 2} = {\bf 4} = {\bf
1}\oplus{\bf 3}$, in which the final step denotes the behaviour under $SO(3)$. Thus by forming a 4-vector of $SO(4)$ out of the rotational singlet and triplet Bell states, the complete, and explicit behaviour given the Wigner angle, of these Bell states under Lorentz transformations can be succinctly stated, as in Eq.(\[e:tyt\]). We therefore advocate for Bell states the convention in Eq.(\[e:con\]). Details of the setup are presented in Section IV. In Section V, we introduce reduced density matrices, defined through Yang’s prescription[@yang], for systems of identical particles; and analyze their behaviour under Lorentz transformations. Without taking Lorentz symmetry into account, quantum correlations and entanglement of identical fermions have also been studied in Refs.[@ekert; @schliemann; @yushi; @paskauskas]. Here we are able to show that the von Neumann entropy of each of the constructed reduced density matrix is Lorentz invariant; and we illustrate the usefulness of the von Neumann entropy as a Lorentz-invariant measure of entanglement with a worked example comparing 