  A four-dimensional photon polarization space, such that gives a different
interpretation of the ladder operators for the time-like degree comparing to
the Gupta-Bleuler formulation is presented. This interpretation, coming from
the construction of a covariant Hamiltonian, gives positive defined norms for
all the four polarization degrees of freedom. This paper is written in the
background of reducible representation algebras introduced by Czachor, although
the interpretation of the ladder operators as presented here could be done
independently. States that reproduce standard electromagnetic fields (i.e.
photons with two transverse polarizations) from the four-dimensional covariant
formalism (i.e. with two additional longitudinal and time-like polarizations)
are shown explicitly. Lastly, Lorentz and gauge transformations are discussed
in detail.
