Duality and helicity: the photon wave function approach

Abstract

The photon wave equation proposed in terms of the Riemann-Silberstein vector is derived from a first-order Dirac/Weyl-type action principle. It is symmetric w.r.t. duality transformations, but the associated Noether quantity vanishes. Replacing the fields by potentials and using instead a quadratic Klein-Gordon-type Lagrangian allows us to recover the double-Chern-Simons expression of conserved helicity and is shown to be equivalent to recently proposed alternative frameworks. Applied to the potential-modified theory the Dirac/Weyl-type approach yields again zero conserved charge, whereas the Klein-Gordon-type approach applied to the original setting yields Lipkin's "zilch".

Title changed, the main result clarified and better explained. References added. 13 pages, 1 Table, no figures. To be published in Phys. Lett. A

References in corpus (5)

• The role of the Riemann-Silberstein vector in classical and quantum theories of electromagnetism
• Dynamical evolution of the chiral magnetic effect: Applications to the quark-gluon plasma
• Spacetime algebra as a powerful tool for electromagnetism
• Electromagnetic duality anomaly in curved spacetimes
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• The Zilch Vortical Effect
• On enhanced sensing of chiral molecules in optical cavities
• Total helicity of electromagnetic fields and matter
• Memory Effect and Carroll Symmetry: 50 years later
• Optical helicity and Hertz vectors
• A conformally invariant derivation of average electromagnetic helicity