  We consider the representations of the optical Dirac equation, especially
ones where the Hamiltonian is purely real-valued. This is equivalent, for
Maxwell's equations, to the Majorana representation of the massless Dirac
(Weyl) equation. We draw analogies between the Dirac, chiral and Majorana
representations of the Dirac and optical Dirac equations, and derive two new
optical Majorana representations. Just as the Dirac and chiral representations
are related to optical spin and helicity states, these Majorana representations
of the optical Dirac equation are associated with the linear polarisation of
light. This provides a means to compare electron and electromagnetic wave
equations in the context of classical field theory.
