Angular momentum decomposition from a QED example

TL;DR

This paper uses a QED example within the light-front formalism to clarify the decomposition of angular momentum, showing that separating fermion and boson contributions for orbital angular momentum measurement is unjustified.

Contribution

It provides an explicit calculation demonstrating the limitations of separating fermion and boson angular momenta in proton spin decomposition.

Findings

Sum of fermion and boson angular momenta equals half the sum of gravitational form factors A(0) and B(0)

Separation of angular momentum into fermion and boson parts for orbital measurements is not justified

Explicit QED example clarifies debates in proton spin decomposition

Abstract

We investigate the angular momentum decomposition with a quantum electrodynamics example to clarify the proton spin decomposition debates. We adopt the light-front formalism where the parton model is well defined. We prove that the sum of fermion and boson angular momenta is equal to half the sum of the two gravitational form factors $A(0)$ and $B(0)$, as is well known. However, the suggestion to make a separation of the above relation into the fermion and boson pieces, as a way to measure the orbital angular momentum of fermions or bosons, respectively, is not justified from our explicit calculation.