The Zilch Electromagnetic Conservation Law Revisited
arXiv:1904.08639 · doi:10.1063/1.5126487
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 real and complex versions of duality-symmetric Maxwell Lagrangians.
arXiv comment15 pages, 1 table, no figures
References in corpus (17)
- Transverse and longitudinal angular momenta of light
- Dual electromagnetism: Helicity, spin, momentum, and angular momentum
- Characterizing optical chirality
- Weak Measurements of Light Chirality with a Plasmonic Slit
- Conservation of the spin and orbital angular momenta in electromagnetism
- Spin and orbital angular momenta of acoustic beams
- Optical momentum and angular momentum in complex media: From the Abraham-Minkowski debate to unusual properties of surface plasmon-polaritons
- Acoustic Radiation Force and Torque on Small Particles as Measures of the Canonical Momentum and Spin Densities
- Electromagnetic helicity in complex media
- Transverse spin and surface waves in acoustic metamaterials
- Spacetime algebra as a powerful tool for electromagnetism
- Lipkin's conservation law, Noether's theorem, and the relation to optical helicity
- Acoustic versus electromagnetic field theory: scalar, vector, spinor representations and the emergence of acoustic spin
- Klein-Gordon representation of acoustic waves and topological origin of surface acoustic modes
- The Zilch Vortical Effect
- Classification of local conservation laws of Maxwell's equations
- Helicity and spin conservation in Maxwell theory and Linearized Gravity
Cited by in corpus (4)
- Energy-momentum tensor and duality symmetry of linearized gravity in the Fierz formalism
- Conservation of all Lipkin's zilches from symmetries of the standard electromagnetic action and a hidden algebra
- Helicity, Spin, and Infra-zilch of Light: a Lorentz Covariant Formulation
- Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics