What Are the Quantum Commutation Relations for the Total Angular Momentum of Light?

The total angular momentum of light has received attention for itsapplication in a variety of phenomena such as optical communication, opticalforces and sensing. However, the quantum behavior including the commutationrelations have been relatively less explored. Here, we derive the correctcommutation relation for the total angular momentum of light using bothrelativistic and non-relativistic approaches. An important outcome of our workis the proof that the widely-assumed quantum commutation relation for the totalobservable angular momentum of light is fundamentally incorrect. Our work willmotivate experiments and leads to new insight on the quantum behavior of theangular momentum of light.