The zilch electromagnetic conservation law revisited
Sajad Aghapour, Lars Andersson, Kjell Rosquist
Abstract
It is shown that the zilch conservation law arises as the Noether current corresponding to a variational symmetry of a duality-symmetric Maxwell Lagrangian. The action of the corresponding symmetry generator on the duality-symmetric Lagrangian, while non-vanishing, is a total divergence as required by the Noether theory. The variational nature of the zilch conservation law was previously known only for some of the components of the zilch tensor, notably the optical chirality. By contrast, our analysis is fully covariant and is, therefore, valid for all components of the zilch tensor. The analysis is presented here for both the real and complex versions of duality-symmetric Maxwell Lagrangians.
Topics & Concepts
Noether's theoremConservation lawDuality (order theory)Mathematical physicsSymmetry (geometry)Covariant transformationTensor (intrinsic definition)LagrangianConserved currentSymmetric tensorPhysicsClassical mechanicsMathematicsQuantum mechanicsExact solutions in general relativityPure mathematicsGeometrySolar and Space Plasma DynamicsQuantum and Classical ElectrodynamicsStellar, planetary, and galactic studies