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

Dirac type relativistic quantum mechanics for massive photons