On the Majorana representation of the optical Dirac equation

TL;DR

This paper explores real-valued Hamiltonian representations of the optical Dirac equation, introducing two new Majorana representations linked to light polarization, and draws analogies with electron wave equations.

Contribution

It introduces two novel optical Majorana representations of the Dirac equation, connecting polarization states with Majorana fermions in classical field theory.

Findings

Derived two new optical Majorana representations.

Linked Majorana representations to light polarization.

Established analogies between electron and optical wave equations.

Abstract

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.