# Angular Momentum Conservation Law in Light-Front Quantum Field Theory

## TL;DR

This paper proves the Lorentz invariance of angular momentum and helicity sum rules in light-front quantum field theory, revealing unique features and deriving selection rules applicable to QED and QCD.

## Contribution

It demonstrates the invariance of the $j^3$ component of angular momentum under Lorentz transformations in the light-front form and derives new selection rules for orbital angular momentum in quantum field theories.

## Key findings

- $j^3$ remains unchanged under Lorentz boosts in light-front form.
- Derived a selection rule for orbital angular momentum in QED and QCD.
- Established an upper bound on orbital angular momentum change in scattering processes.

## Abstract

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.