\begin{pmatrix}
    1      & & {\bm 0}  \\  \\
    \bm{0} & & \cos\theta\delta_{ij} +\epsilon_{ijk}(\sin\theta)\hat \theta^k +
    (1-\cos\theta)\hat \theta^i
    \hat \theta^j
  \end{pmatrix};$$ which means that, as expected, the three Bell states ${\ensuremath{|B^{1,2,3}({\ensuremath{\textbf p}}_1,
{\ensuremath{\textbf p}}_2)\rangle}}$ form an $SO(3)$ [*rotation triplet*]{} while ${\ensuremath{|B^0({\ensuremath{\textbf p}}_1, {\ensuremath{\textbf p}}_2)\rangle}}$ is a [*singlet*]{}. For an equal-mass entangled pair in the center-of-momentum(COM) frame (${\ensuremath{\textbf p}}_1 + {\ensuremath{\textbf p}}_2 = 0$) and pure boost in the perpendicular direction (${\bm\tau}\cdot{\ensuremath{\textbf p}}_{1,2} = 0$), Eqs. (A9)-(A13) of Appendix A reveal that the resultant Wigner rotations are related by $\bm\phi(\bm\tau,{\ensuremath{\textbf p}}_1) = -\bm\phi({\bm\tau},{\ensuremath{\textbf p}}_2)\equiv \bm\phi$. Thus with (${\textbf{X}}= {\textbf{Y}}= \bm\phi$) the result is $$R_\nu^{~\mu} =
  \begin{pmatrix}
    \cos\phi             & & (\sin\phi)\hat{\phi^j} \\  \\
    -(\sin\phi)\hat{\phi^i} & & \delta_{ij}+(\cos\phi - 1)\hat \phi^i\hat \phi^j
  \end{pmatrix}.$$ In general, rotational singlet and triplet states do not belong to invariant subspaces when boost transformations are also included. Special cases of the behaviour of Bell states for massive particles under Lorentz transformations have also been calculated in Refs.[@milburn; @ahn; @terashima]. As we have shown the precise and complete behaviour under [*arbitrary*]{} Lorentz transformations can be succinctly stated, as in Eq.([\[e:tyt\]]{}).

Two-particle states as superpositions of Bell states
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In the previous sections we discussed Bell states with infinitely sharp momenta, 