  We present in this paper how the single-photon wave function for transversal
photons (with the direct sum of ordinary unitary representations of helicity 1
and -1 acting on it) is subsumed within the formalism of Gupta-Bleuler for the
quantized free electromagnetic field in the Krein space (i.e. in the ordinary
Hilbert space endowed with the Gupta-Bleuler operator $\eta$). Rigorous
Gupta-Bleuler quantization of the free electromagnetic field is based on a
generalization of ours (published formerly) of the Mackey theory of induced
representations which includes representations preserving the indefinite Krein
inner-product given by the Gupta-Bleuler operator and acting in the Krein
space. The free electromagnetic field is constructed by application of the
Segal's second quantization functor to the specific Krein-isometric
representation. A closed subspace $\mathcal{H}_{\textrm{tr}}$ of the
single-photon Krein space on which the indefinite Krein-inner-product is
strictly positive is constructed such that the Krein-isometric single-photon
representation generates modulo unphysical states precisely the action of a
representation which preserves the positive inner product on
$\mathcal{H}_{\textrm{tr}}$ induced by the Krein inner product, and is equal to
the direct sum of ordinary unitary representations of helicity 1 and -1
respectively. Two states of single photon Krein space are physically equivalent
whenever differ by a state of Krein norm zero and whose projection on
$\mathcal{H}_{\textrm{tr}}$, in the sense of the Krein-inner-product, vanishes.
In particulart it follows that the results of Bia{\l}ynicki-Birula on the
single-photon wave function may be reconciled with the micro-local perturbative
approach to QED initiated by St\"uckelberg and Bogoliubov.
