Optical helicity, optical spin and related quantities in electromagnetic theory

We examine the optical helicity, the optical spin and the ij-infra- zilches in electromagnetic theory and show that these conserved quantities can be combined to form a new description of the angular momentum associated with optical polarization: one that is analogous to the familiar description of optical energy and linear momentum. The symmetries of Maxwell’s equations that underlie the conservation of our quantities are presented and discussed. We explain that a similar but distinct set of quantities, Lipkin’s zilches, describe the ‘angular momentum’ of the curl of the electromagnetic field, rather than the angular momentum of the electromagnetic field itself.