New angular momentum conservation laws for electromagnetic waves interacting with Dirac fields

Abstract Global conservation laws of angular momentum (AM) are well-known in the theory of light–matter interaction. However, local conservation laws, i.e. the conservation law of AM at every point in space, remain unexplored especially in the context of relativistic Dirac–Maxwell fields. Here, we use the QED Lagrangian and Noether’s theorem to derive a new local conservation law of AM for Dirac–Maxwell fields in the form of the continuity relation for linear momentum. We separate this local conservation law into four coupled motion equations for spin and orbital AM (OAM) densities. We introduce a helicity current tensor, OAM current tensor, and spin–orbit torque in the motion equations to shed light on the local dynamics of spin-OAM interaction and AM exchange between Maxwell and Dirac fields. We elucidate how our results translate to classical electrodynamics using the example of plane wave interference as well as a dual-mode optical fiber. Our results shine light on AM phenomena related to the relativistic interaction of electromagnetic waves and Dirac fields.