Solution
= Solution
Both terms in $B_\mu=W_\mu-\frac14\bar Q\bar\sigma_\mu Q$ commute with momentum. For the first,
$$
[W_\mu,P_\rho]=\frac12\epsilon_{\mu\nu\lambda\sigma}
[M^{\nu\lambda},P_\rho]P^\sigma=0,
$$
because the two resulting products of momenta are symmetric in indices contracted with the <Levi-Civita symbol>. For the second, $[P_\rho,Q]=[P_\rho,\bar Q]=0$. Therefore
$$
\boxed{[B_\mu,P_\rho]=0}.
$$