{\ensuremath{\mathbb I}}+ {\ensuremath{\frac{i}{2}}}\left[ \omega_{ij}-\frac{1}{p^0+m}(p_i\omega_{j0}-p_j\omega_{i0})\right]
  M^{ij}\\
  &=& {\ensuremath{\mathbb I}}+ i{\bm\theta}_W\cdot{\bm J},\end{aligned}$$ with the infinitesimal Wigner angle denoted as $$\label{w1}
  \bm\theta_W  = \bm\theta-\frac{{\ensuremath{\textbf p}}\times
  {\ensuremath{\bm\tau}}}{p^0+m} \equiv \bm\theta + {\bm\phi}_1.$$ This agrees with the results of Ref.[@ohnuki] when rotations and boosts are considered separately. It should be noted that the generators of the Wigner [*rotations*]{} are indeed $J_i = \frac{1}{2}\epsilon_{ijk}M^{jk}$, but the complete Wigner angle receives contributions from both the boost and rotation parameters, $\tau^i= \omega^i\,_0$ and $\theta_i =
\frac{1}{2}\epsilon_{ijk}\omega^{jk}$ respectively, of $\Lambda(\omega)$. In the absence of boosts, Wigner rotations are degenerate with ordinary rotations i.e. $\bm\theta_W =\bm\theta$. Although arbitrary finite Lorentz transformations of $\Lambda(\omega) =
\exp({\ensuremath{\frac{i}{2}}}{\omega_{\alpha\beta}}M^{\alpha\beta})$ can be evaluated as $\lim_{N \rightarrow \infty} [{\ensuremath{\mathbb I}}+
\frac{i}{2}\frac{\omega_{\alpha\beta}}{N}M^{\alpha\beta}]^{N}$, it is not simple to express the corresponding finite Wigner rotations in closed form via products of infinitesimal rotations, essentially because Wigner rotations are also functions of the momenta. We may however consider a general Lorentz transformation relating two frames as a product of a pure boost in an arbitrary direction, $L({\bm\alpha})= \exp(-i{\bm\alpha}\cdot{\bf K})$, followed by an arbitrary rotation $R({\bm\psi})$. Using the multiplication rule for Wigner transformations, (Eq.(\[e:multi\]) in Appendix A), the closed form Wigner rotation can be expressed as in Eqs.(A16)-(A17). Note also that for 