  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.
