On the Majorana representation of the optical Dirac equation

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 polarization of light. This provides a means to compare electron and electromagnetic wave equations in the context of classical field theory.

Automated summary

This study investigates the representations of the optical Dirac equation, particularly those with a purely real-valued Hamiltonian. For Maxwell's equations, this is equivalent to the Majorana representation of the massless Dirac (Weyl) equation. Analogies are drawn between the Dirac, chiral, and Majorana representations of the Dirac and optical Dirac equations, leading to the derivation of two new optical Majorana representations. These representations are associated with the linear polarization of light and provide a means to compare electron and electromagnetic wave equations in the context of classical field theory.