Electric–magnetic symmetry and Noether's theorem

Abstract

In the absence of charges, Maxwell's equations are highly symmetrical. In particular, they place the electric and magnetic fields on equal footing. In light of this electric–magnetic symmetry, we introduce a variational description of the free electromagnetic field that is based upon the acknowledgement of both electric and magnetic potentials. We use our description, together with Noether's theorem, to demonstrate that electric–magnetic symmetry is, in essence, an expression of the conservation of optical helicity. The symmetry associated with the conservation of Lipkin's zilches is also identified. We conclude by considering, with care, the subtle separation of the rotation and boost angular momenta of the field into their ‘spin’ and ‘orbital’ contributions.