Angular Momentum Conservation Law in Light-Front Quantum Field Theory

Understand

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.