Conservation laws and symmetry transformations of the electromagnetic field with sources

In classical electrodynamics, the universal conservation laws of energy, momentum, and angular momentum are expressed by well-known continuity equations for the densities of these quantities. In the presence of charges and currents source terms must be added. These terms describe the exchange of energy and (linear or angular) momentum between field and matter. Recently, other conserved quantities of the electromagnetic field have been introduced and discussed. Examples are the pseudoscalars chirality and helicity, which are related to the handedness of the field. Even though these quantities have no obvious definition for matter, their conservation laws can still be presented in the form of continuity equations with source terms added. We show that these terms shed light on the interaction of chiral light with matter. A different role of conserved quantities is that they generate symmetry transformations of the system. The spatial transformations translation and rotation of the radiation field are generated by differential operators acting on mode functions. These operators are identical in form to the operators for the momentum and angular momentum of a quantum particle with spin 1. Also, for the total helicity and spin angular momentum of the field such operators on mode functions can be identified. A quite different picture arises in a quantum description of the electromagnetic field. The operator nature of the conserved quantities then arises from the commutation rules of photon creation and annihilation operators. We analyze the relation between these two pictures of symmetry transformations of the electromagnetic field.