if we denote the spin $\frac{1}{2}$ doublet as the ${\bf 2}$ of $SU(2)$, then a 2-particle state behaves as $${\bf 2}\otimes{\bf 2} = {\bf 4} = {\bf 1}\oplus{\bf3} \,$$ where the final step denotes its behaviour under $SO(3)$. In other words, we may express the two-particle state in terms of a four-vector (the $\bf 4$) of $SO(4)$ which transforms as singlet and triplet states under $SO(3)$. Indeed it is known the four Bell states are expressible as a singlet and a triplet under ordinary 3-dimensional $SO(3)$ rotations, and as we shall show, they undergo $SO(4)$ Wigner rotations among themselves under Lorentz transformations.

The quadruplet $(\mu =0,1,2,3)$ of Bell states can be conveniently defined in the following manner: $$\label{e:con}
  {\ensuremath{|B^\mu({\ensuremath{\textbf p}}_1,{\ensuremath{\textbf p}}_2)\rangle}} \equiv \frac{1}{\sqrt{2}}({\ensuremath{\tilde\sigma}}^\mu\sigma^2)_{s s'}
  a^\dag({\ensuremath{\textbf p}}_1,s; n_1)a^\dag({\ensuremath{\textbf p}}_2,s';n_2){\ensuremath{|0\rangle}}$$ with ${\ensuremath{\tilde\sigma}}^0 = i{\ensuremath{\mathbb I}}_2$ and ${\ensuremath{\tilde\sigma}}^i (i=1,2,3)$ being the Pauli matrices $\sigma^i$. In discussing an entangled pair of identical as well as distinguishable particles, the additional species labels, $n_{1,2}$, can be introduced for generality. Let us proceed to show that the states defined above are indeed Bell states. The spin indices $s, s'$ are summed over $\pm\frac{1}{2}$ (which we shall denote as $\pm$ for simplicity). Focusing on the spin part of 