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".
Cite
@article{arxiv.1608.08573,
title = {Duality and helicity: the photon wave function approach},
author = {M. Elbistan and P. A. Horvathy and P. -M. Zhang},
journal= {arXiv preprint arXiv:1608.08573},
year = {2017}
}
Comments
Title changed, the main result clarified and better explained. References added. 13 pages, 1 Table, no figures. To be published in Phys. Lett. A