I am concerned about generators of the Poincare Lie Group that is responsible for boosts and rotations (often labelled by $J_{\nu \mu}$).
$J_{\nu \mu}$ is often divided into a term responsible for the spin angular momentum ($S_{\nu \mu}$) and another term responsible for the orbital angular momentum ($L_{\nu \mu}$). Therefore,
$J_{\nu \mu}$ = $L_{\nu \mu}$ + $S_{\nu \mu}$
I am wondering why is the $S_{0 \mu}$ components equal to zero?