Lorentz covariance of optical Dirac equation and spinorial photon field

Abstract

In a recent paper (2014 New J. Phys. 16 093008) Barnett discussed the so-called optical Dirac equation and referred to the involved wave function as a spinor. But as he claimed explicitly, he did not really associate that wave function with a true spinor. Here we show that if the optical Dirac equation is interpreted as the dynamical equation for the photon in conventional quantum mechanics, the wave function, called the photon field, does transform under the Lorentz transformation as a spinor. For the optical Dirac equation to be Lorentz covariant, however, a constraint on the photon field is required, which can be cast into the form of Maxwell’s divergence equations. It is found that the spinorial photon field not only satisfies the principle of locality but also has the right dimensionality as is required by conventional quantum mechanics.