What are the quantum commutation relations for the total angular momentum of light?

TL;DR

This paper derives the correct quantum commutation relations for the total angular momentum of light, revealing that widely-used assumptions are fundamentally incorrect, which impacts understanding and future experiments in quantum optics.

Contribution

The paper provides the first derivation of the correct quantum commutation relations for the total angular momentum of light, challenging previous assumptions.

Findings

Established the correct quantum commutation relations for light's angular momentum

Proved that common assumptions about these relations are incorrect

Motivates new experimental investigations in quantum optics

Abstract

The total angular momentum of light has received attention for its application in a variety of phenomena such as optical communication, optical forces and sensing. However, the quantum behavior including the commutation relations have been relatively less explored. Here, we derive the correct commutation relation for the total angular momentum of light using both relativistic and non-relativistic approaches. An important outcome of our work is the proof that the widely-assumed quantum commutation relation for the total observable angular momentum of light is fundamentally incorrect. Our work will motivate experiments and leads to new insight on the quantum behavior of the angular momentum of light.