Dirac type relativistic quantum mechanics for massive photons

TL;DR

This paper develops a relativistic quantum mechanics framework for massive photons without quantum field theory, predicting the existence of anti-photons and establishing a consistent probability density and covariance.

Contribution

It introduces a new RQM for massive photons that includes negative energy solutions and anti-photons, distinct from traditional field-theoretic models.

Findings

Predicts anti-photons analogous to positrons

Constructs a positive definite probability density

Confirms Lorentz covariance of the equations

Abstract

Constructing a relativistic quantum mechanics (RQM) for a massive photon, without appealing to the quantum field theoretical approach such as the massive Proca model, we find a new theoretical particle solution which allows the massive photon having either positive or negative energy as solutions. In particular, we predict the existence of the so-called anti-photon corresponding to the negative energy solution, similar to the positron in the Dirac RQM for an electron. Note that the anti-photons could be an intense radiation flare of the gamma ray burst. In this RQM for the massive photon, we construct a positive definite probability density and a nontrivial diagonal Hamiltonian, and also discuss a massless photon. Moreover we confirm the covariances of the relativistic equation of motion for the massive photon and the corresponding probability continuity equation under the Lorentz transformation.