General Description of Relativistic States

In spite of the successes of the Dirac equation and of its usefulness in the construction of relativistic quantum fields (to be discussed later, in Sect. 8), there is little doubt that the wave function formalism for relativistic particles is not quite satisfactory. First of all, the meaning of the variables r and t in a wave function Ψ(r,t) is unclear; as we will show, r does not represent the position for a Dirac particle, and in fact a position operator does not even exist, strictu senso, for a photon. As for t, the interpretation of it as the time becomes less clear when we have several particles: which time? The proper time of each of the particles? Time as measured in the centre of mass reference system?