Spinor wave equation of photon

TL;DR

This paper derives covariant spinor wave equations for free and unfree photons, linking them to specific Lorentz group representations, advancing the theoretical understanding of photon quantum states.

Contribution

It introduces new covariant spinor wave equations for photons, connecting them to Lorentz group representations, which is a novel theoretical development.

Findings

Derived spinor wave equations for free photons.

Established covariance of the equations under Lorentz transformations.

Linked spinor solutions to specific Lorentz group representations.

Abstract

In this paper, we give the spinor wave equations of free and unfree photon, which are the differential equation of space-time one order. For the free photon, the spinor wave equations are covariant, and the spinors $\psi$ are corresponding to the the reducibility representations $D^{10}+D^{01}$ and $D^{10}+D^{01}+D^{1/2 1/2}$ of the proper Lorentz group.