  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".

High Energy Physics - Theory;Classical Physics;Quantum Physics