  Electromagnetic waves carry an infinite number of conserved quantities. We
give a simple explanation of this fact, which also shows how to write down
conserved quantities at will and calculate their associated symmetry
transformations. This framework is then used to discuss decompositions of
optical angular momentum, and to prove that magnetic helicity is conserved for
beams and pulses. Finally we describe an infinite set of electromagnetic
conserved quantities that corresponds to the Virasoro generators of conformal
field theories. In the quantum case the Virasoro generators acquire a central
charge in their algebra, an example of a quantum anomaly.
