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Electromagnetic waves carry an infinite number of conserved quantities. Wegive a simple explanation of this fact, which also shows how to write downconserved quantities at will and calculate their associated symmetrytransformations. This framework is then used to discuss decompositions ofoptical angular momentum, and to prove that magnetic helicity is conserved forbeams and pulses. Finally we describe an infinite set of electromagneticconserved quantities that corresponds to the Virasoro generators of conformalfield theories. In the quantum case the Virasoro generators acquire a centralcharge in their algebra, an example of a quantum anomaly.

A note on conserved quantities for electromagnetic waves