  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.
