  We prove the Lorentz invariance of the angular momentum conservation law and
the helicity sum rule for relativistic composite systems in the light-front
formulation. We explicitly show that $j^3$, the $z$-component of the angular
momentum remains unchanged under Lorentz transformations generated by the
light-front kinematical boost operators. The invariance of $j^3$ under Lorentz
transformations is a feature unique to the front form. Applying the Lorentz
invariance of the angular quantum number in the front form, we obtain a
selection rule for the orbital angular momentum which can be used to eliminate
certain interaction vertices in QED and QCD. We also generalize the selection
rule to any renormalizable theory and show that there exists an upper bound on
the change of orbital angular momentum in scattering processes at any fixed
order in perturbation theory.
