{\bm J} +{\ensuremath{\textbf p}}\times\frac{\partial}{i\partial{\ensuremath{\textbf p}}} \\
  \vec{{\ensuremath{\mathbb K}}} &=& (\frac{{\bm
J}\times{\ensuremath{\textbf p}}}{p^0+m} + p^0\frac{\partial}{i\partial{\ensuremath{\textbf p}}} +
  \frac{{\ensuremath{\textbf p}}}{2ip^0}),\label{e:46}\end{aligned}$$ do satisfy the commutation relations of the Lie algebra of the Lorentz group: $$\label{e:loco}
    [{{\ensuremath{\mathbb J}}}^i, {{\ensuremath{\mathbb J}}}^j]= i\epsilon^{ijk}{{\ensuremath{\mathbb J}}}^k, \qquad [{{\ensuremath{\mathbb J}}}^i, {{\ensuremath{\mathbb K}}}^j]=
    i\epsilon^{ijk}{{\ensuremath{\mathbb K}}}^k, \qquad
    [{{\ensuremath{\mathbb K}}}^i, {{\ensuremath{\mathbb K}}}^j]= -i\epsilon^{ijk}{{\ensuremath{\mathbb J}}}^k.$$ Likewise ${\ensuremath{\mathbb M}}^{\mu\nu}$ of Eqs.(3.14) and (3.15) obey the similar commutation relations. The expression of the boost generator of Ref.[@czachor] (following Ref.[@ohnuki]) and Ref.[@terno] which differs from ours in not having the final term of Eq.(\[e:46\]) can be rendered Hermitian provided the measure $d^3{{\ensuremath{\textbf p}}}/p^0$ is adopted instead of Weinberg’s.

Bell States and Lorentz transformations
=======================================

In this section we specialize to the case with ${\bm J} = {\bm\sigma}/{2}$ for spin $\frac{1}{2}$ particles. For each massive spin $\frac{1}{2}$ particle, the Lie group of all Wigner rotations is $SU(2)$. A two-particle state, and in particular an entangled Bell pair, should transform according to the $SU(2)\times{SU(2)}$ representation. As we shall see, the isomorphism between $[SU(2)\times{SU(2)}]/{Z_2}$ and $SO(4)$ permits us to describe the behaviour of the four basis Bell states of spin space for fixed momenta under Lorentz transformations succinctly. Since $SO(3)$ is a subgroup of $SO(4)$, in group theoretical terms 